एक सर्वे में (n(U)=210), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=39), (n\(B\cap C\)=31), (n\(C\cap A\)=28) और (n\(A\cap B\cap C\)=14) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?
In a survey (n(U)=210), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=39), (n\(B\cap C\)=31), (n\(C\cap A\)=28) and (n\(A\cap B\cap C\)=14). How many are in none of the sets?
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#venn-diagrams
#three-sets
#complement
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A (36)
B (174)
C (50)
D (64)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), so outside is (210-174=36). First find the union and then take the complement.
Step 2
Why this answer is correct
The correct answer is A. (36). (n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), so outside is (210-174=36). First find the union and then take the complement.
Step 3
Exam Tip
(n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), इसलिए बाहर (210-174=36) है। पहले संघ निकालकर ही पूरक लें।
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यदि (n\(A\cup B\cup C\)=155), (n\(A\cup B\)=118), (n\(B\cup C\)=124), (n\(C\cup A\)=121) और (n(B)=64) है, तो (n(\(A\cap C\)-B)) कितना होगा?
If (n\(A\cup B\cup C\)=155), (n\(A\cup B\)=118), (n\(B\cup C\)=124), (n\(C\cup A\)=121) and (n(B)=64), then what is (n(\(A\cap C\)-B))?
#sets
#venn-diagrams
#compound-region
#expert
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A (30)
B (27)
C (34)
D (37)
Explanation opens after your attempt
Step 1
Concept
(n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23), not (30). Check the formula before matching options.
Step 2
Why this answer is correct
The correct answer is A. (30). (n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23), not (30). Check the formula before matching options.
Step 3
Exam Tip
(n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23) नहीं, इसलिए विकल्पों से पहले सूत्र जाँचें; सही क्षेत्र (155-118) और (155-124) जैसे बाहर वाले हिस्सों से नहीं निकलेगा।
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यदि (n(A)=78), (n(B)=69), (n(C)=63), (n\(A\cap B\)=30), (n\(B\cap C\)=25), (n\(C\cap A\)=21) और (n\(A\cap B\cap C\)=9) है, तो केवल (A) में कितने तत्व हैं?
If (n(A)=78), (n(B)=69), (n(C)=63), (n\(A\cap B\)=30), (n\(B\cap C\)=25), (n\(C\cap A\)=21) and (n\(A\cap B\cap C\)=9), then how many elements are only in (A)?
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#only-a
#three-sets
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A (36)
B (27)
C (48)
D (57)
Explanation opens after your attempt
Step 1
Concept
Only (A=78-30-21+9=36). In three sets, the centre is subtracted twice, so add it back.
Step 2
Why this answer is correct
The correct answer is A. (36). Only (A=78-30-21+9=36). In three sets, the centre is subtracted twice, so add it back.
Step 3
Exam Tip
केवल (A=78-30-21+9=36) है। तीन समुच्चयों में केंद्र दो बार घटता है इसलिए उसे वापस जोड़ें।
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किसी वेन आरेख में केवल (A) में (18), केवल (B) में (22), केवल (C) में (16), केवल \(A\cap B\) में (11), केवल \(B\cap C\) में (13), केवल \(C\cap A\) में (9) और तीनों में (6) तत्व हैं। कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?
In a Venn diagram, only (A) has (18), only (B) has (22), only (C) has (16), only \(A\cap B\) has (11), only \(B\cap C\) has (13), only \(C\cap A\) has (9), and all three have (6) elements. How many elements are in at least two sets?
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#at-least-two
#regions
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A (39)
B (33)
C (56)
D (95)
Explanation opens after your attempt
Step 1
Concept
At least two sets contain (11+13+9+6=39) elements. In this type of question, the centre region is also included.
Step 2
Why this answer is correct
The correct answer is A. (39). At least two sets contain (11+13+9+6=39) elements. In this type of question, the centre region is also included.
Step 3
Exam Tip
कम से कम दो में (11+13+9+6=39) तत्व हैं। इस प्रकार के प्रश्न में तीनों वाला केंद्र भी शामिल होता है।
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यदि (n\(A\cup B\)=112), (n(A-B)=43) और (n(B-A)=37) है, तो (n\(A\cap B\)) कितना होगा?
If (n\(A\cup B\)=112), (n(A-B)=43) and (n(B-A)=37), then what is (n\(A\cap B\))?
#sets
#venn-diagrams
#two-sets
#intersection
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A (32)
B (75)
C (80)
D (69)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of three disjoint parts, so the intersection is (112-43-37=32). Count each separate region once in a Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. (32). The union is the sum of three disjoint parts, so the intersection is (112-43-37=32). Count each separate region once in a Venn diagram.
Step 3
Exam Tip
संघ तीन अलग भागों का योग है, इसलिए प्रतिच्छेद (112-43-37=32) है। वेन आरेख में अलग क्षेत्रों को एक-एक बार गिनें।
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यदि (n(U)=140), (n(A')=58), (n(B')=71) और (n\(A\cap B\)=34) है, तो (n\(A\cup B\)) कितना है?
If (n(U)=140), (n(A')=58), (n(B')=71) and (n\(A\cap B\)=34), then what is (n\(A\cup B\))?
#sets
#venn-diagrams
#complement
#union
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A (117)
B (105)
C (82)
D (69)
Explanation opens after your attempt
Step 1
Concept
(n(A)=140-58=82) and (n(B)=140-71=69), so the union is (82+69-34=117). Getting original sizes from complements is the first step.
Step 2
Why this answer is correct
The correct answer is A. (117). (n(A)=140-58=82) and (n(B)=140-71=69), so the union is (82+69-34=117). Getting original sizes from complements is the first step.
Step 3
Exam Tip
(n(A)=140-58=82) और (n(B)=140-71=69), इसलिए संघ (82+69-34=117) है। पूरक से मूल संख्या निकालना पहला कदम है।
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यदि (n\(A\cap B'\)=29), (n\(A'\cap B\)=33), (n\(A\cap B\)=17) और (n(\(A\cup B\)')=21) है, तो (n(U)) कितना है?
If (n\(A\cap B'\)=29), (n\(A'\cap B\)=33), (n\(A\cap B\)=17) and (n(\(A\cup B\)')=21), then what is (n(U))?
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#venn-diagrams
#partition
#universal-set
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A (100)
B (79)
C (83)
D (121)
Explanation opens after your attempt
Step 1
Concept
The sum of all four disjoint regions is (29+33+17+21=100). The universal set includes both inside and outside regions.
Step 2
Why this answer is correct
The correct answer is A. (100). The sum of all four disjoint regions is (29+33+17+21=100). The universal set includes both inside and outside regions.
Step 3
Exam Tip
सभी चार अलग क्षेत्रों का योग (29+33+17+21=100) है। सार्वत्रिक समुच्चय में अंदर और बाहर दोनों क्षेत्र आते हैं।
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एक कक्षा में (95) विद्यार्थियों में (56) गणित, (49) विज्ञान और (27) दोनों पढ़ते हैं। ठीक एक विषय पढ़ने वाले कितने हैं?
In a class of (95) students, (56) study Mathematics, (49) study Science and (27) study both. How many study exactly one subject?
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#exactly-one
#word-problem
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A (51)
B (78)
C (22)
D (68)
Explanation opens after your attempt
Step 1
Concept
Exactly one subject is ((56-27)+(49-27)=51). Do not include those who study both in exactly one.
Step 2
Why this answer is correct
The correct answer is A. (51). Exactly one subject is ((56-27)+(49-27)=51). Do not include those who study both in exactly one.
Step 3
Exam Tip
ठीक एक विषय ((56-27)+(49-27)=51) है। दोनों पढ़ने वालों को ठीक एक में शामिल न करें।
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यदि (n(A)=64), (n(B)=59) और (n\(A\cup B\)=91) है, तो (n\(A\triangle B\)) कितना है?
If (n(A)=64), (n(B)=59) and (n\(A\cup B\)=91), then what is (n\(A\triangle B\))?
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#symmetric-difference
#union
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A (59)
B (32)
C (91)
D (123)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cap B\)=64+59-91=32), then (n\(A\triangle B\)=91-32=59). The symmetric difference does not include the common part.
Step 2
Why this answer is correct
The correct answer is A. (59). First (n\(A\cap B\)=64+59-91=32), then (n\(A\triangle B\)=91-32=59). The symmetric difference does not include the common part.
Step 3
Exam Tip
पहले (n\(A\cap B\)=64+59-91=32), फिर (n\(A\triangle B\)=91-32=59) है। सममित अंतर में साझा भाग नहीं आता।
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यदि \(A\subseteq B\), (n(B)=83), (n(A)=47) और (n(U)=120) है, तो (n(B-A)) कितना होगा?
If \(A\subseteq B\), (n(B)=83), (n(A)=47) and (n(U)=120), then what is (n(B-A))?
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#subset
#difference
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A (36)
B (47)
C (83)
D (37)
Explanation opens after your attempt
Step 1
Concept
Since \(A\subseteq B\), (B-A=83-47=36). In a subset Venn diagram, the smaller circle lies inside the larger one.
Step 2
Why this answer is correct
The correct answer is A. (36). Since \(A\subseteq B\), (B-A=83-47=36). In a subset Venn diagram, the smaller circle lies inside the larger one.
Step 3
Exam Tip
क्योंकि \(A\subseteq B\), इसलिए (B-A=83-47=36) होगा। उपसमुच्चय वाले वेन आरेख में छोटा वृत्त बड़े के अंदर होता है।
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यदि \(A\cap B=\varnothing\), (n(A)=44), (n(B)=52) और (n(U)=130) है, तो (n(\(A\cup B\)')) कितना है?
If \(A\cap B=\varnothing\), (n(A)=44), (n(B)=52) and (n(U)=130), then what is (n(\(A\cup B\)'))?
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#venn-diagrams
#disjoint
#complement
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A (34)
B (96)
C (78)
D (86)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, the union is (44+52=96), so the complement is (130-96=34). Disjoint sets have zero common part.
Step 2
Why this answer is correct
The correct answer is A. (34). For disjoint sets, the union is (44+52=96), so the complement is (130-96=34). Disjoint sets have zero common part.
Step 3
Exam Tip
असंबद्ध समुच्चयों में संघ (44+52=96) है, इसलिए पूरक (130-96=34) है। असंबद्ध होने पर साझा भाग शून्य होता है।
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तीन क्लबों में (n(A)=72), (n(B)=68), (n(C)=61), (n\(A\cap B\)=29), (n\(B\cap C\)=24), (n\(C\cap A\)=26) और (n\(A\cap B\cap C\)=11) है। केवल (B) में आने वाले सदस्य कितने हैं?
In three clubs (n(A)=72), (n(B)=68), (n(C)=61), (n\(A\cap B\)=29), (n\(B\cap C\)=24), (n\(C\cap A\)=26) and (n\(A\cap B\cap C\)=11). How many members are only in (B)?
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#only-b
#three-sets
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A (26)
B (15)
C (39)
D (44)
Explanation opens after your attempt
Step 1
Concept
Only (B=68-29-24+11=26). While subtracting two intersections, the centre is removed twice.
Step 2
Why this answer is correct
The correct answer is A. (26). Only (B=68-29-24+11=26). While subtracting two intersections, the centre is removed twice.
Step 3
Exam Tip
केवल (B=68-29-24+11=26) है। दो प्रतिच्छेद घटाते समय केंद्र दो बार घट जाता है।
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यदि (n\(A\cup B\cup C\)=135), ठीक एक समुच्चय में (58) और ठीक दो समुच्चयों में (49) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?
If (n\(A\cup B\cup C\)=135), exactly one set has (58) elements and exactly two sets have (49) elements, then what is (n\(A\cap B\cap C\))?
#sets
#venn-diagrams
#triple-intersection
#exactly-two
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A (28)
B (86)
C (77)
D (49)
Explanation opens after your attempt
Step 1
Concept
Union equals exactly one plus exactly two plus all three, so all three is (135-58-49=28). In region-based questions, keep the parts separate.
Step 2
Why this answer is correct
The correct answer is A. (28). Union equals exactly one plus exactly two plus all three, so all three is (135-58-49=28). In region-based questions, keep the parts separate.
Step 3
Exam Tip
संघ (=) ठीक एक (+) ठीक दो (+) तीनों है, इसलिए तीनों (135-58-49=28) हैं। क्षेत्र आधारित प्रश्नों में भागों को अलग रखें।
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यदि (n(A)=5x+4), (n(B)=4x+7), (n\(A\cap B\)=2x+3) और (n\(A\cup B\)=78) है, तो (x) का मान क्या है?
If (n(A)=5x+4), (n(B)=4x+7), (n\(A\cap B\)=2x+3) and (n\(A\cup B\)=78), then what is the value of (x)?
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#venn-diagrams
#algebra
#two-sets
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A (10)
B (9)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
(78=(5x+4)+(4x+7)-(2x+3)=7x+8), so (x=10). In algebraic questions, apply the union formula directly.
Step 2
Why this answer is correct
The correct answer is A. (10). (78=(5x+4)+(4x+7)-(2x+3)=7x+8), so (x=10). In algebraic questions, apply the union formula directly.
Step 3
Exam Tip
(78=(5x+4)+(4x+7)-(2x+3)=7x+8), इसलिए (x=10) है। बीजगणितीय प्रश्न में संघ का सूत्र सीधे लगाएँ।
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यदि (n(A-B)=3x+2), (n(B-A)=2x+5), (n\(A\cap B\)=x+4) और (n\(A\cup B\)=71) है, तो (x) कितना है?
If (n(A-B)=3x+2), (n(B-A)=2x+5), (n\(A\cap B\)=x+4) and (n\(A\cup B\)=71), then what is (x)?
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#venn-diagrams
#algebra
#regions
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A (10)
B (8)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The union is (3x+2+2x+5+x+4=6x+11=71), so (x=10). The sum of disjoint regions directly gives the union.
Step 2
Why this answer is correct
The correct answer is A. (10). The union is (3x+2+2x+5+x+4=6x+11=71), so (x=10). The sum of disjoint regions directly gives the union.
Step 3
Exam Tip
संघ (3x+2+2x+5+x+4=6x+11=71), इसलिए (x=10) है। अलग क्षेत्रों का योग सीधे संघ देता है।
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यदि \(U={1,2,\ldots,72}\), (A) (6) के गुणजों का और (B) (8) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?
If \(U={1,2,\ldots,72}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (8), then what is (n\(A\cap B\))?
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#venn-diagrams
#multiples
#lcm
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Common multiples are multiples of (\operatorname{lcm}(6,8)=24), namely (24,48,72). Hence the count is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). Common multiples are multiples of (\operatorname{lcm}(6,8)=24), namely (24,48,72). Hence the count is (3).
Step 3
Exam Tip
साझा गुणज (\operatorname{lcm}(6,8)=24) के गुणज होंगे, जो (24,48,72) हैं। इसलिए संख्या (3) है।
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यदि \(U={1,2,\ldots,90}\), (A) (5) के गुणजों का और (B) (9) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) कितना होगा?
If \(U={1,2,\ldots,90}\), (A) is the set of multiples of (5) and (B) is the set of multiples of (9), then what is (n\(A\cup B\))?
#sets
#venn-diagrams
#multiples
#union
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A (26)
B (28)
C (18)
D (10)
Explanation opens after your attempt
Step 1
Concept
Multiples of (5) are (18), multiples of (9) are (10), and multiples of (45) are (2), so the union is (18+10-2=26). Do not count common multiples twice.
Step 2
Why this answer is correct
The correct answer is A. (26). Multiples of (5) are (18), multiples of (9) are (10), and multiples of (45) are (2), so the union is (18+10-2=26). Do not count common multiples twice.
Step 3
Exam Tip
(5) के गुणज (18), (9) के गुणज (10), और (45) के गुणज (2) हैं, इसलिए संघ (18+10-2=26) है। साझा गुणजों को दोबारा न गिनें।
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यदि \(U={1,2,\ldots,84}\), (A) (7) के गुणजों का और (B) (4) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना है?
If \(U={1,2,\ldots,84}\), (A) is the set of multiples of (7) and (B) is the set of multiples of (4), then what is (n(\(A\cup B\)'))?
#sets
#venn-diagrams
#multiples
#complement
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A (54)
B (30)
C (57)
D (63)
Explanation opens after your attempt
Step 1
Concept
Multiples of (7) are (12), multiples of (4) are (21), and multiples of (28) are (3), so the union is (30) and the complement is (84-30=54).
Step 2
Why this answer is correct
The correct answer is A. (54). Multiples of (7) are (12), multiples of (4) are (21), and multiples of (28) are (3), so the union is (30) and the complement is (84-30=54).
Step 3
Exam Tip
(7) के गुणज (12), (4) के गुणज (21), और (28) के गुणज (3) हैं, इसलिए संघ (30) और पूरक (84-30=54) है।
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यदि \(U={1,2,\ldots,40}\), (A) अभाज्य संख्याओं का और (B) सम संख्याओं का समुच्चय है, तो \(A\cap B\) क्या है?
If \(U={1,2,\ldots,40}\), (A) is the set of prime numbers and (B) is the set of even numbers, then what is \(A\cap B\)?
#sets
#venn-diagrams
#prime-numbers
#intersection
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A ({2})
B \(\varnothing\)
C ({2,4,6})
D ({3,5,7})
Explanation opens after your attempt
Step 1
Concept
The only even prime is (2), so \(A\cap B={2}\). In an intersection, both conditions must be satisfied together.
Step 2
Why this answer is correct
The correct answer is A. ({2}). The only even prime is (2), so \(A\cap B={2}\). In an intersection, both conditions must be satisfied together.
Step 3
Exam Tip
सम अभाज्य संख्या केवल (2) है, इसलिए \(A\cap B={2}\) है। प्रतिच्छेद में दोनों शर्तें साथ में पूरी होनी चाहिए।
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यदि \(U={1,2,\ldots,36}\), (A) वर्ग संख्याओं का और (B) (3) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?
If \(U={1,2,\ldots,36}\), (A) is the set of square numbers and (B) is the set of multiples of (3), then what is (n\(A\cap B\))?
#sets
#venn-diagrams
#square-numbers
#intersection
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Square numbers are (1,4,9,16,25,36), and the square multiples of (3) are (9,36). Therefore, the intersection has (2) elements.
Step 2
Why this answer is correct
The correct answer is A. (2). Square numbers are (1,4,9,16,25,36), and the square multiples of (3) are (9,36). Therefore, the intersection has (2) elements.
Step 3
Exam Tip
वर्ग संख्याएँ (1,4,9,16,25,36) हैं और (3) के गुणज वर्ग (9,36) हैं। इसलिए प्रतिच्छेद में (2) तत्व हैं।
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\(यदि (A={x:x\in \mathbb{N},x\le 20}), (B={x:x\) is odd\(,x\le 20}) और (C={x:x\) is a multiple of \(5,x\le 20}) है, तो (n(B\cap C)) कितना है\)?
\(If (A={x:x\in \mathbb{N},x\le 20}), (B={x:x\) is odd\(,x\le 20}) and (C={x:x\) is a multiple of \(5,x\le 20}), then what is (n(B\cap C))\)?
#sets
#venn-diagrams
#set-builder
#intersection
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A (2)
B (4)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(B\cap C\) contains (5) and (15), so the count is (2). In set-builder form, check the conditions together.
Step 2
Why this answer is correct
The correct answer is A. (2). \(B\cap C\) contains (5) and (15), so the count is (2). In set-builder form, check the conditions together.
Step 3
Exam Tip
\(B\cap C\) में (5) और (15) आते हैं, इसलिए संख्या (2) है। समुच्चय-निर्माण रूप में शर्तों को एक साथ जाँचें।
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यदि (n(U)=75), (n(A)=46), (n(B)=41) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान कितना है?
If (n(U)=75), (n(A)=46), (n(B)=41), then what is the minimum possible value of (n\(A\cap B\))?
#sets
#venn-diagrams
#minimum-intersection
#expert
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A (12)
B (0)
C (34)
D (41)
Explanation opens after your attempt
Step 1
Concept
The minimum intersection is (46+41-75=12). When the sum of two sets exceeds (U), overlap is necessary.
Step 2
Why this answer is correct
The correct answer is A. (12). The minimum intersection is (46+41-75=12). When the sum of two sets exceeds (U), overlap is necessary.
Step 3
Exam Tip
न्यूनतम प्रतिच्छेद (46+41-75=12) है। जब दोनों का योग (U) से अधिक हो तो अतिव्यापन अनिवार्य होता है।
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यदि (n(A)=73) और (n(B)=58) है, तो (n\(A\cap B\)) का अधिकतम संभव मान कितना है?
If (n(A)=73) and (n(B)=58), then what is the maximum possible value of (n\(A\cap B\))?
#sets
#venn-diagrams
#maximum-intersection
#expert
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A (58)
B (73)
C (131)
D (15)
Explanation opens after your attempt
Step 1
Concept
The intersection cannot be larger than the smaller set, so the maximum is (58). In the maximum case, the smaller set may lie inside the larger set.
Step 2
Why this answer is correct
The correct answer is A. (58). The intersection cannot be larger than the smaller set, so the maximum is (58). In the maximum case, the smaller set may lie inside the larger set.
Step 3
Exam Tip
प्रतिच्छेद छोटे समुच्चय से बड़ा नहीं हो सकता, इसलिए अधिकतम (58) है। अधिकतम स्थिति में छोटा समुच्चय बड़े के भीतर हो सकता है।
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यदि (n(U)=150), (n(A)=91), (n(B)=86) है, तो (n\(A\cup B\)) का न्यूनतम संभव मान कितना है?
If (n(U)=150), (n(A)=91), (n(B)=86), then what is the minimum possible value of (n\(A\cup B\))?
#sets
#venn-diagrams
#minimum-union
#subset
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A (91)
B (86)
C (150)
D (177)
Explanation opens after your attempt
Step 1
Concept
The minimum union can be as small as the larger set, which is (91). This is possible when \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. (91). The minimum union can be as small as the larger set, which is (91). This is possible when \(B\subseteq A\).
Step 3
Exam Tip
संघ का न्यूनतम मान बड़े समुच्चय जितना हो सकता है, यानी (91)। ऐसा तब संभव है जब \(B\subseteq A\) हो।
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यदि (n(A)=42), (n(B)=38) और (n\(A\cap B\)=17) है, तो (n\(A'\cap B\)) कितना है?
If (n(A)=42), (n(B)=38) and (n\(A\cap B\)=17), then what is (n\(A'\cap B\))?
#sets
#venn-diagrams
#complement
#difference
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A (21)
B (25)
C (55)
D (17)
Explanation opens after your attempt
Step 1
Concept
\(A'\cap B\) means (B-A), so it is (38-17=21). Connect the notation with the only (B) region in the Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. (21). \(A'\cap B\) means (B-A), so it is (38-17=21). Connect the notation with the only (B) region in the Venn diagram.
Step 3
Exam Tip
\(A'\cap B\) का अर्थ (B-A) है, इसलिए (38-17=21) है। प्रतीक को वेन आरेख के केवल (B) क्षेत्र से जोड़कर देखें।
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यदि (n(A)=55), (n(B)=62), (n(A-B)=23) है, तो (n\(A\cup B\)) कितना है?
If (n(A)=55), (n(B)=62), (n(A-B)=23), then what is (n\(A\cup B\))?
#sets
#venn-diagrams
#difference
#union
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A (85)
B (117)
C (94)
D (39)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=55-23=32), so (n\(A\cup B\)=55+62-32=85). First find the common part and then the union.
Step 2
Why this answer is correct
The correct answer is A. (85). (n\(A\cap B\)=55-23=32), so (n\(A\cup B\)=55+62-32=85). First find the common part and then the union.
Step 3
Exam Tip
(n\(A\cap B\)=55-23=32), इसलिए (n\(A\cup B\)=55+62-32=85) है। पहले साझा भाग खोजें फिर संघ निकालें।
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यदि (n\(A\cup B\)=98) और (n\(A\cap B\)=35) है, तो (n(A-B)+n(B-A)) कितना होगा?
If (n\(A\cup B\)=98) and (n\(A\cap B\)=35), then what is (n(A-B)+n(B-A))?
#sets
#venn-diagrams
#only-regions
#symmetric-difference
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A (63)
B (133)
C (35)
D (98)
Explanation opens after your attempt
Step 1
Concept
The sum of the two only regions is (98-35=63). This is also the size of \(A\triangle B\).
Step 2
Why this answer is correct
The correct answer is A. (63). The sum of the two only regions is (98-35=63). This is also the size of \(A\triangle B\).
Step 3
Exam Tip
दोनों केवल क्षेत्रों का योग (98-35=63) है। यह \(A\triangle B\) की संख्या भी होती है।
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वेन आरेख में (A-\(B\cap C\)) कौन सा क्षेत्र दर्शाता है?
Which region does (A-\(B\cap C\)) represent in a Venn diagram?
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#set-difference
#compound-region
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A (A) का वह भाग जो \(B\cap C\) में नहीं है / The part of (A) not in \(B\cap C\)
B सिर्फ \(B\cap C\) / Only \(B\cap C\)
C पूरा \(A\cap B\cap C\) / Whole \(A\cap B\cap C\)
D सिर्फ (A') / Only (A')
Explanation opens after your attempt
Correct Answer
A. (A) का वह भाग जो \(B\cap C\) में नहीं है / The part of (A) not in \(B\cap C\)
Step 1
Concept
(A-\(B\cap C\)) contains elements of (A) that are not in \(B\cap C\). In a Venn diagram, remove the subtracted region.
Step 2
Why this answer is correct
The correct answer is A. (A) का वह भाग जो \(B\cap C\) में नहीं है / The part of (A) not in \(B\cap C\). (A-\(B\cap C\)) contains elements of (A) that are not in \(B\cap C\). In a Venn diagram, remove the subtracted region.
Step 3
Exam Tip
(A-\(B\cap C\)) में (A) के वे तत्व हैं जो \(B\cap C\) में नहीं हैं। वेन आरेख में घटाने वाला क्षेत्र हटाकर देखें।
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यदि \(A\subseteq B\), तो (\(A\cup B\)-A) किसके बराबर होगा?
If \(A\subseteq B\), then (\(A\cup B\)-A) is equal to what?
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#venn-diagrams
#subset
#simplification
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A (B-A)
B (A)
C (B)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Since \(A\subseteq B\), \(A\cup B=B\), and (\(A\cup B\)-A=B-A). In subset problems, simplify the union first.
Step 2
Why this answer is correct
The correct answer is A. (B-A). Since \(A\subseteq B\), \(A\cup B=B\), and (\(A\cup B\)-A=B-A). In subset problems, simplify the union first.
Step 3
Exam Tip
क्योंकि \(A\subseteq B\), इसलिए \(A\cup B=B\), और (\(A\cup B\)-A=B-A) है। उपसमुच्चय में पहले संघ को सरल करें।
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यदि \(A\cap B=A\) और \(A\neq \varnothing\) है, तो कौन सा संबंध सही है?
If \(A\cap B=A\) and \(A\neq \varnothing\), which relation is correct?
#sets
#venn-diagrams
#subset
#reasoning
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A\cap B=\varnothing\)
D \(A\cup B=A\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
If the common part is the whole of (A), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). If the common part is the whole of (A), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.
Step 3
Exam Tip
यदि साझा भाग पूरा (A) है, तो (A) पूरी तरह (B) में है। इसलिए \(A\subseteq B\) सही है।
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यदि \(A\cap B=\varnothing\), तो (A-B) किसके बराबर होगा?
If \(A\cap B=\varnothing\), then (A-B) is equal to what?
#sets
#venn-diagrams
#disjoint
#difference
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A (A)
B \(\varnothing\)
C (B)
D \(A\cup B\)
Explanation opens after your attempt
Step 1
Concept
When (A) and (B) have no common element, removing (B) from (A) leaves (A) unchanged. Therefore, (A-B=A).
Step 2
Why this answer is correct
The correct answer is A. (A). When (A) and (B) have no common element, removing (B) from (A) leaves (A) unchanged. Therefore, (A-B=A).
Step 3
Exam Tip
जब (A) और (B) में कोई साझा तत्व नहीं है, तो (B) को हटाने पर (A) वैसा ही रहता है। इसलिए (A-B=A) है।
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यदि (n\(A\cup B\)=n(A)), तो वेन आरेख के अनुसार कौन सा निष्कर्ष सही है?
If (n\(A\cup B\)=n(A)), which conclusion is correct according to the Venn diagram?
#sets
#venn-diagrams
#subset
#union
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D (A=B')
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
The union is the same size as (A), meaning (B) adds no new region. Therefore, \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). The union is the same size as (A), meaning (B) adds no new region. Therefore, \(B\subseteq A\).
Step 3
Exam Tip
संघ (A) जितना ही है, इसका अर्थ (B) से कोई नया क्षेत्र नहीं जुड़ रहा। इसलिए \(B\subseteq A\) है।
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यदि (n\(A\cap B\)=0) और (n(A)=28), (n(B)=34) है, तो (n\(A\triangle B\)) कितना है?
If (n\(A\cap B\)=0) and (n(A)=28), (n(B)=34), then what is (n\(A\triangle B\))?
#sets
#venn-diagrams
#symmetric-difference
#disjoint
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A (62)
B (34)
C (28)
D (6)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, the symmetric difference is the whole union, so (28+34=62). When the common part is zero, nothing needs to be removed.
Step 2
Why this answer is correct
The correct answer is A. (62). For disjoint sets, the symmetric difference is the whole union, so (28+34=62). When the common part is zero, nothing needs to be removed.
Step 3
Exam Tip
असंबद्ध समुच्चयों में सममित अंतर पूरा संघ होता है, इसलिए (28+34=62) है। साझा भाग शून्य होने पर कुछ हटाना नहीं पड़ता।
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किसी सर्वे में (120) लोगों में (66) अखबार पढ़ते हैं, (58) पत्रिका पढ़ते हैं और (24) कोई भी नहीं पढ़ते। दोनों पढ़ने वाले कितने हैं?
In a survey of (120) people, (66) read a newspaper, (58) read a magazine and (24) read neither. How many read both?
#sets
#venn-diagrams
#survey
#intersection
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A (28)
B (96)
C (4)
D (42)
Explanation opens after your attempt
Step 1
Concept
At least one is (120-24=96), so both is (66+58-96=28). First remove the outside part to get the union.
Step 2
Why this answer is correct
The correct answer is A. (28). At least one is (120-24=96), so both is (66+58-96=28). First remove the outside part to get the union.
Step 3
Exam Tip
कम से कम एक (120-24=96) है, इसलिए दोनों (66+58-96=28) हैं। पहले बाहर वाले भाग को हटाकर संघ निकालें।
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एक परीक्षा में (150) विद्यार्थियों में (82) ने प्रश्न (A), (76) ने प्रश्न (B), (69) ने प्रश्न (C), (37) ने (A) और (B), (32) ने (B) और (C), (29) ने (C) और (A), तथा (15) ने तीनों हल किए। कम से कम एक प्रश्न हल करने वाले कितने हैं?
In an exam, among (150) students, (82) solved question (A), (76) solved question (B), (69) solved question (C), (37) solved (A) and (B), (32) solved (B) and (C), (29) solved (C) and (A), and (15) solved all three. How many solved at least one question?
#sets
#venn-diagrams
#three-sets
#exam-survey
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A (144)
B (129)
C (135)
D (150)
Explanation opens after your attempt
Step 1
Concept
At least one is (82+76+69-37-32-29+15=144). In three sets, do not forget to add the centre at the end.
Step 2
Why this answer is correct
The correct answer is A. (144). At least one is (82+76+69-37-32-29+15=144). In three sets, do not forget to add the centre at the end.
Step 3
Exam Tip
कम से कम एक (82+76+69-37-32-29+15=144) है। तीन समुच्चयों में केंद्र को अंत में जोड़ना न भूलें।
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यदि (n\(A\cap B\)=26) और (n\(A\cap B\cap C\)=10) है, तो केवल \(A\cap B\) में कितने तत्व हैं?
If (n\(A\cap B\)=26) and (n\(A\cap B\cap C\)=10), then how many elements are only in \(A\cap B\)?
#sets
#venn-diagrams
#only-pair
#triple-intersection
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A (16)
B (26)
C (36)
D (10)
Explanation opens after your attempt
Step 1
Concept
Only \(A\cap B\) has (26-10=16) elements. A two-set intersection includes the central three-set region too.
Step 2
Why this answer is correct
The correct answer is A. (16). Only \(A\cap B\) has (26-10=16) elements. A two-set intersection includes the central three-set region too.
Step 3
Exam Tip
केवल \(A\cap B\) में (26-10=16) तत्व होंगे। दो-समुच्चय प्रतिच्छेद में तीनों वाला केंद्र भी शामिल रहता है।
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यदि केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (12), केवल \(C\cap A\) में (15) और \(A\cap B\cap C\) में (8) तत्व हैं, तो (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))) कितना है?
If only \(A\cap B\) has (14), only \(B\cap C\) has (12), only \(C\cap A\) has (15), and \(A\cap B\cap C\) has (8) elements, then what is (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\)))?
#sets
#venn-diagrams
#pairwise-union
#at-least-two
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A (49)
B (41)
C (57)
D (35)
Explanation opens after your attempt
Step 1
Concept
This region is the part belonging to at least two sets, so (14+12+15+8=49). Add the centre only once.
Step 2
Why this answer is correct
The correct answer is A. (49). This region is the part belonging to at least two sets, so (14+12+15+8=49). Add the centre only once.
Step 3
Exam Tip
यह क्षेत्र कम से कम दो समुच्चयों का भाग है, इसलिए (14+12+15+8=49) है। केंद्र को केवल एक बार जोड़ें।
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यदि केवल (A) में (31), केवल (B) में (27), केवल (C) में (25), केवल दो-दो के कुल भाग में (42) और तीनों में (11) हैं, तो (n\(A\cup B\cup C\)) कितना है?
If only (A) has (31), only (B) has (27), only (C) has (25), the total of exactly two-set regions is (42), and all three have (11), then what is (n\(A\cup B\cup C\))?
#sets
#venn-diagrams
#regions
#union
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A (136)
B (125)
C (94)
D (147)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of all disjoint regions (31+27+25+42+11=136). Do not add any region twice in a Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. (136). The union is the sum of all disjoint regions (31+27+25+42+11=136). Do not add any region twice in a Venn diagram.
Step 3
Exam Tip
संघ सभी अलग क्षेत्रों का योग (31+27+25+42+11=136) है। वेन आरेख में कोई क्षेत्र दो बार न जोड़ें।
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यदि (n(A)=70), (n(B)=65), (n(C)=60), (n\(A\cup B\cup C\)=128), (n\(A\cap B\)=27), (n\(B\cap C\)=24), (n\(C\cap A\)=22) है, तो (n\(A\cap B\cap C\)) कितना है?
If (n(A)=70), (n(B)=65), (n(C)=60), (n\(A\cup B\cup C\)=128), (n\(A\cap B\)=27), (n\(B\cap C\)=24), (n\(C\cap A\)=22), then what is (n\(A\cap B\cap C\))?
#sets
#venn-diagrams
#unknown-triple
#equation
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A (6)
B (12)
C (18)
D (11)
Explanation opens after your attempt
Step 1
Concept
Using (128=70+65+60-27-24-22+x), we get (x=6). Let the unknown centre be (x) and form an equation.
Step 2
Why this answer is correct
The correct answer is A. (6). Using (128=70+65+60-27-24-22+x), we get (x=6). Let the unknown centre be (x) and form an equation.
Step 3
Exam Tip
सूत्र में (128=70+65+60-27-24-22+x), इसलिए (x=6) है। अज्ञात केंद्र को (x) मानकर समीकरण बनाएं।
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यदि (n(A\cap\(B\cup C\))=44), केवल \(A\cap B\) में (18) और केवल \(A\cap C\) में (16) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?
If (n(A\cap\(B\cup C\))=44), only \(A\cap B\) has (18) and only \(A\cap C\) has (16) elements, then what is (n\(A\cap B\cap C\))?
#sets
#venn-diagrams
#compound-region
#triple-intersection
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A (10)
B (8)
C (34)
D (44)
Explanation opens after your attempt
Step 1
Concept
(A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (44-18-16=10).
Step 2
Why this answer is correct
The correct answer is A. (10). (A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (44-18-16=10).
Step 3
Exam Tip
(A\cap\(B\cup C\)) में केवल \(A\cap B\), केवल \(A\cap C\) और केंद्र आते हैं, इसलिए केंद्र (44-18-16=10) है।
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कौन सा कथन \(A\cap(B-C)\) के वेन क्षेत्र को सही बताता है?
Which statement correctly describes the Venn region of \(A\cap(B-C)\)?
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#venn-diagrams
#compound-region
#difference
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A वे तत्व जो (A) और (B) में हैं पर (C) में नहीं हैं / Elements in (A) and (B) but not in (C)
B वे तत्व जो केवल (C) में हैं / Elements only in (C)
C वे तत्व जो \(A\cup B\cup C\) से बाहर हैं / Elements outside \(A\cup B\cup C\)
D वे तत्व जो तीनों में हैं / Elements in all three
Explanation opens after your attempt
Correct Answer
A. वे तत्व जो (A) और (B) में हैं पर (C) में नहीं हैं / Elements in (A) and (B) but not in (C)
Step 1
Concept
(B-C) has elements of (B) not in (C), and then the common part with (A) is taken. So it is the only \(A\cap B\) region.
Step 2
Why this answer is correct
The correct answer is A. वे तत्व जो (A) और (B) में हैं पर (C) में नहीं हैं / Elements in (A) and (B) but not in (C). (B-C) has elements of (B) not in (C), and then the common part with (A) is taken. So it is the only \(A\cap B\) region.
Step 3
Exam Tip
(B-C) में (B) के वे तत्व हैं जो (C) में नहीं हैं, और फिर (A) से साझा भाग लिया जाता है। इसलिए यह केवल \(A\cap B\) वाला भाग है।
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यदि (A), (B) और (C) परस्पर असंबद्ध हैं, (n(A)=18), (n(B)=24), (n(C)=29) और (n(U)=90) है, तो (n(\(A\cup B\cup C\)')) कितना है?
If (A), (B) and (C) are mutually disjoint, (n(A)=18), (n(B)=24), (n(C)=29) and (n(U)=90), then what is (n(\(A\cup B\cup C\)'))?
#sets
#venn-diagrams
#mutually-disjoint
#complement
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A (19)
B (71)
C (42)
D (61)
Explanation opens after your attempt
Step 1
Concept
For mutually disjoint sets, the union is (18+24+29=71), so the complement is (90-71=19). In disjoint sets, no common part is subtracted.
Step 2
Why this answer is correct
The correct answer is A. (19). For mutually disjoint sets, the union is (18+24+29=71), so the complement is (90-71=19). In disjoint sets, no common part is subtracted.
Step 3
Exam Tip
परस्पर असंबद्ध होने पर संघ (18+24+29=71) है, इसलिए पूरक (90-71=19) है। असंबद्ध समुच्चयों में कोई साझा भाग नहीं घटता।
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यदि (A), (B) और (C) के लिए \(A\subseteq B\subseteq C\) है, तो \(A\cup B\cup C\) किसके बराबर होगा?
If (A), (B) and (C) satisfy \(A\subseteq B\subseteq C\), then \(A\cup B\cup C\) is equal to what?
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#venn-diagrams
#nested-sets
#union
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A (C)
B (A)
C (B)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
All sets are inside (C), so their union is (C). In a subset chain, the largest set gives the union.
Step 2
Why this answer is correct
The correct answer is A. (C). All sets are inside (C), so their union is (C). In a subset chain, the largest set gives the union.
Step 3
Exam Tip
सभी समुच्चय (C) के भीतर हैं, इसलिए उनका संघ (C) ही होगा। उपसमुच्चय श्रृंखला में सबसे बड़ा समुच्चय संघ देता है।
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यदि \(A\subseteq B\subseteq C\) है, तो \(A\cap B\cap C\) किसके बराबर होगा?
If \(A\subseteq B\subseteq C\), then \(A\cap B\cap C\) is equal to what?
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#venn-diagrams
#nested-sets
#intersection
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A (A)
B (B)
C (C)
D (C-A)
Explanation opens after your attempt
Step 1
Concept
The smallest set (A) is common to all three sets. Therefore, \(A\cap B\cap C=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). The smallest set (A) is common to all three sets. Therefore, \(A\cap B\cap C=A\).
Step 3
Exam Tip
सबसे छोटा समुच्चय (A) तीनों में समान रूप से मौजूद है। इसलिए \(A\cap B\cap C=A\) है।
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यदि (n(A-B)=0) और (n(A)>0) है, तो वेन आरेख में कौन सा संबंध सही होगा?
If (n(A-B)=0) and (n(A)>0), which relation is correct in the Venn diagram?
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#subset
#difference
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A\cap B=\varnothing\)
D \(A\cup B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
(A-B=0) means no part of (A) lies outside (B). Therefore, \(A\subseteq B\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). (A-B=0) means no part of (A) lies outside (B). Therefore, \(A\subseteq B\) is correct.
Step 3
Exam Tip
(A-B=0) का अर्थ (A) का कोई भाग (B) से बाहर नहीं है। इसलिए \(A\subseteq B\) सही है।
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यदि (n\(A\cup B\cup C\)=160), (n(A)=70), (n(B)=75), (n(C)=80) और (n\(A\cap B\cap C\)=18) है, तो (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\)) कितना है?
If (n\(A\cup B\cup C\)=160), (n(A)=70), (n(B)=75), (n(C)=80) and (n\(A\cap B\cap C\)=18), then what is (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\))?
#sets
#venn-diagrams
#pairwise-sum
#inclusion-exclusion
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A (83)
B (65)
C (101)
D (225)
Explanation opens after your attempt
Step 1
Concept
Using the formula (160=70+75+80-S+18), so (S=83). Here (S) is the sum of the three pairwise intersections.
Step 2
Why this answer is correct
The correct answer is A. (83). Using the formula (160=70+75+80-S+18), so (S=83). Here (S) is the sum of the three pairwise intersections.
Step 3
Exam Tip
सूत्र से (160=70+75+80-S+18), इसलिए (S=83) है। यहाँ (S) तीनों युग्म प्रतिच्छेदों का योग है।
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यदि (n(A-B)=20), (n(B-C)=18) और (n(C-A)=16) ही दिए गए हैं, तो क्या केवल इनसे (n\(A\cup B\cup C\)) निश्चित किया जा सकता है?
If only (n(A-B)=20), (n(B-C)=18) and (n(C-A)=16) are given, can (n\(A\cup B\cup C\)) be determined uniquely?
#sets
#venn-diagrams
#insufficient-data
#reasoning
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A नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed
B हाँ, मान (54) है / Yes, the value is (54)
C हाँ, मान (0) है / Yes, the value is (0)
D हाँ, मान (20) है / Yes, the value is (20)
Explanation opens after your attempt
Correct Answer
A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed
Step 1
Concept
These differences do not give information about all regions. The union needs both only-regions and common regions.
Step 2
Why this answer is correct
The correct answer is A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed. These differences do not give information about all regions. The union needs both only-regions and common regions.
Step 3
Exam Tip
इन अंतरों से सभी क्षेत्रों की जानकारी नहीं मिलती। संघ के लिए केवल और साझा दोनों प्रकार के क्षेत्रों की जरूरत होती है।
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अभिकथन: (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\))। कारण: \(A\cap B\) के तत्व (n(A)+n(B)) में दो बार गिने जाते हैं। सही विकल्प चुनें।
Assertion: (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Reason: Elements of \(A\cap B\) are counted twice in (n(A)+n(B)). Choose the correct option.
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#venn-diagrams
#assertion-reason
#formula
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A अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
B अभिकथन सही है पर कारण गलत है / Assertion is true but reason is false
C अभिकथन गलत है पर कारण सही है / Assertion is false but reason is true
D दोनों गलत हैं / Both are false
Explanation opens after your attempt
Correct Answer
A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
Step 1
Concept
Both statements are true, and the reason explains why the intersection is subtracted. In Venn diagrams, identifying double counting of the common region is essential.
Step 2
Why this answer is correct
The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. Both statements are true, and the reason explains why the intersection is subtracted. In Venn diagrams, identifying double counting of the common region is essential.
Step 3
Exam Tip
दोनों कथन सही हैं और कारण बताता है कि प्रतिच्छेद क्यों घटाते हैं। वेन आरेख में साझा क्षेत्र की दोहरी गिनती पहचानना जरूरी है।
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अभिकथन: यदि \(A\cap B=\varnothing\), तो (n\(A\cup B\)=n(A)+n(B))। कारण: असंबद्ध समुच्चयों का कोई साझा क्षेत्र नहीं होता। सही विकल्प चुनें।
Assertion: If \(A\cap B=\varnothing\), then (n\(A\cup B\)=n(A)+n(B)). Reason: Disjoint sets have no common region. Choose the correct option.
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#assertion-reason
#disjoint
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A अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
B अभिकथन सही है पर कारण गलत है / Assertion is true but reason is false
C अभिकथन गलत है पर कारण सही है / Assertion is false but reason is true
D दोनों गलत हैं / Both are false
Explanation opens after your attempt
Correct Answer
A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
Step 1
Concept
For disjoint sets, the intersection is (0), so the union is the direct sum. The reason correctly explains the assertion.
Step 2
Why this answer is correct
The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. For disjoint sets, the intersection is (0), so the union is the direct sum. The reason correctly explains the assertion.
Step 3
Exam Tip
असंबद्ध होने पर प्रतिच्छेद (0) होता है, इसलिए संघ सीधा योग होता है। कारण अभिकथन की सही व्याख्या करता है।
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किसी वेन आरेख में (n\(A\cup B\cup C\)=190), (n(\(A\cup B\cup C\)')=25), और ठीक दो समुच्चयों में (54) तत्व हैं। यदि (n(U)) पूछा जाए, तो उत्तर क्या होगा?
In a Venn diagram, (n\(A\cup B\cup C\)=190), (n(\(A\cup B\cup C\)')=25), and exactly two sets have (54) elements. If (n(U)) is asked, what is the answer?
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#venn-diagrams
#universal-set
#extra-data
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A (215)
B (190)
C (244)
D (165)
Explanation opens after your attempt
Step 1
Concept
The universal set (U) is the sum of the union and the outside region, so (190+25=215). The exactly-two data is extra here.
Step 2
Why this answer is correct
The correct answer is A. (215). The universal set (U) is the sum of the union and the outside region, so (190+25=215). The exactly-two data is extra here.
Step 3
Exam Tip
सार्वत्रिक समुच्चय (U) संघ और उसके बाहर वाले भाग का योग है, इसलिए (190+25=215) है। ठीक दो वाला आंकड़ा इस प्रश्न में अनावश्यक है।
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