वेन आरेख में पूरा आयत किसको दिखाता है?
What does the whole rectangle show in a Venn diagram?
#sets
#venn-diagrams
#universal-set
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A सार्वत्रिक समुच्चय (U) / Universal set (U)
B समुच्चय (A) / Set (A)
C समुच्चय (B) / Set (B)
D रिक्त समुच्चय \(\varnothing\) / Empty set \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. सार्वत्रिक समुच्चय (U) / Universal set (U)
Step 1
Concept
The whole rectangle shows the universal set (U). In a Venn diagram, all circles are drawn inside (U).
Step 2
Why this answer is correct
The correct answer is A. सार्वत्रिक समुच्चय (U) / Universal set (U). The whole rectangle shows the universal set (U). In a Venn diagram, all circles are drawn inside (U).
Step 3
Exam Tip
पूरा आयत सार्वत्रिक समुच्चय (U) को दिखाता है। वेन आरेख में सभी वृत्त (U) के अंदर बनते हैं।
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यदि (n(A)=26), (n(B)=18), और (n\(A\cap B\)=8), तो वेन आरेख के अनुसार (n\(A\cup B\)) क्या है?
If (n(A)=26), (n(B)=18), and (n\(A\cap B\)=8), then according to the Venn diagram what is (n\(A\cup B\))?
#sets
#venn-diagrams
#union
#counting
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A (36)
B (44)
C (52)
D (16)
Explanation opens after your attempt
Step 1
Concept
Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), we get (26+18-8=36). The common part must be subtracted once.
Step 2
Why this answer is correct
The correct answer is A. (36). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), we get (26+18-8=36). The common part must be subtracted once.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से (26+18-8=36) मिलता है। साझा भाग को एक बार घटाना जरूरी है।
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दो वृत्तों के बीच का साझा भाग किसका क्षेत्र होता है?
The common region between two circles is the region of what?
#sets
#venn-diagrams
#intersection
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A (A-B)
B \(A\cap B\)
C \(A\cup B\)
D (A')
Explanation opens after your attempt
Correct Answer
B. \(A\cap B\)
Step 1
Concept
The common region is called \(A\cap B\). Intersection contains elements that are in both sets.
Step 2
Why this answer is correct
The correct answer is B. \(A\cap B\). The common region is called \(A\cap B\). Intersection contains elements that are in both sets.
Step 3
Exam Tip
साझा भाग \(A\cap B\) कहलाता है। प्रतिच्छेद में वही अवयव आते हैं जो दोनों समुच्चयों में हों।
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यदि (n(U)=58) और (n\(A\cup B\)=41), तो वेन आरेख में न (A) न (B) वाले क्षेत्र में कितने अवयव होंगे?
If (n(U)=58) and (n\(A\cup B\)=41), how many elements will be in the region neither in (A) nor in (B) in the Venn diagram?
#sets
#venn-diagrams
#neither
#complement
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A (17)
B (41)
C (58)
D (99)
Explanation opens after your attempt
Step 1
Concept
The region neither in (A) nor in (B) is (\(A\cup B\)'), so the number is (58-41=17). It is outside both circles but inside (U).
Step 2
Why this answer is correct
The correct answer is A. (17). The region neither in (A) nor in (B) is (\(A\cup B\)'), so the number is (58-41=17). It is outside both circles but inside (U).
Step 3
Exam Tip
न (A) न (B) वाला क्षेत्र (\(A\cup B\)') है, इसलिए संख्या (58-41=17) होगी। यह दोनों वृत्तों के बाहर लेकिन (U) के अंदर का भाग है।
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वेन आरेख में दोनों वृत्तों के बाहर लेकिन (U) के अंदर का भाग किससे लिखा जाता है?
In a Venn diagram, how is the region outside both circles but inside (U) written?
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#venn-diagrams
#neither
#complement
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A \(A\cup B\)
B \(A\cap B\)
C (\(A\cup B\)')
D (A-B)
Explanation opens after your attempt
Correct Answer
C. (\(A\cup B\)')
Step 1
Concept
The region outside both circles is (\(A\cup B\)'). It is also called the neither (A) nor (B) region.
Step 2
Why this answer is correct
The correct answer is C. (\(A\cup B\)'). The region outside both circles is (\(A\cup B\)'). It is also called the neither (A) nor (B) region.
Step 3
Exam Tip
दोनों वृत्तों के बाहर का भाग (\(A\cup B\)') होता है। इसे न (A) न (B) वाला क्षेत्र भी कहते हैं।
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यदि \(A\subseteq B\), तो वेन आरेख में (A) का क्षेत्र किसके अंदर होगा?
If \(A\subseteq B\), inside which region will (A) lie in a Venn diagram?
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#subset
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A (B) के अंदर / Inside (B)
B (B) के बाहर / Outside (B)
C (U) के बाहर / Outside (U)
D (A') के अंदर / Inside (A')
Explanation opens after your attempt
Correct Answer
A. (B) के अंदर / Inside (B)
Step 1
Concept
\(A\subseteq B\) means every element of (A) is in (B). So the circle of (A) will lie inside (B).
Step 2
Why this answer is correct
The correct answer is A. (B) के अंदर / Inside (B). \(A\subseteq B\) means every element of (A) is in (B). So the circle of (A) will lie inside (B).
Step 3
Exam Tip
\(A\subseteq B\) का अर्थ है कि (A) का हर अवयव (B) में है। इसलिए (A) का वृत्त (B) के अंदर होगा।
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यदि (A) और (B) में कोई साझा अवयव नहीं है, तो वेन आरेख में वे कैसे दिखेंगे?
If (A) and (B) have no common element, how will they appear in a Venn diagram?
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#venn-diagrams
#disjoint-sets
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A एक दूसरे को काटते हुए / Intersecting each other
B अलग-अलग वृत्तों के रूप में / As separate circles
C एक ही वृत्त के रूप में / As the same circle
D (U) के बाहर / Outside (U)
Explanation opens after your attempt
Correct Answer
B. अलग-अलग वृत्तों के रूप में / As separate circles
Step 1
Concept
When there is no common element, \(A\cap B=\varnothing\). Therefore, their circles are drawn separately.
Step 2
Why this answer is correct
The correct answer is B. अलग-अलग वृत्तों के रूप में / As separate circles. When there is no common element, \(A\cap B=\varnothing\). Therefore, their circles are drawn separately.
Step 3
Exam Tip
कोई साझा अवयव न होने पर \(A\cap B=\varnothing\) होता है। इसलिए उनके वृत्त अलग-अलग बनते हैं।
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यदि (n(A)=14), (n(B)=10), और (n\(A\cap B\)=3), तो (n\(A\cup B\)) क्या है?
If (n(A)=14), (n(B)=10), and (n\(A\cap B\)=3), what is (n\(A\cup B\))?
#sets
#venn-diagrams
#union-count
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A (17)
B (21)
C (24)
D (27)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=14+10-3=21). In union, the common part is subtracted once.
Step 2
Why this answer is correct
The correct answer is B. (21). (n\(A\cup B\)=14+10-3=21). In union, the common part is subtracted once.
Step 3
Exam Tip
(n\(A\cup B\)=14+10-3=21)। संघ में साझा भाग को एक बार घटाते हैं।
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यदि (n(A)=19), (n(B)=13), और (n\(A\cup B\)=25), तो (n\(A\cap B\)) क्या है?
If (n(A)=19), (n(B)=13), and (n\(A\cup B\)=25), what is (n\(A\cap B\))?
#sets
#venn-diagrams
#intersection-count
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A (5)
B (7)
C (12)
D (32)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=19+13-25=7). To find intersection, subtract the union from the sum of both sets.
Step 2
Why this answer is correct
The correct answer is B. (7). (n\(A\cap B\)=19+13-25=7). To find intersection, subtract the union from the sum of both sets.
Step 3
Exam Tip
(n\(A\cap B\)=19+13-25=7)। प्रतिच्छेद निकालते समय दोनों समुच्चयों के योग से संघ घटाएं।
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यदि (n(U)=38) और (n(A)=16), तो (n(A')) क्या होगा?
If (n(U)=38) and (n(A)=16), what will (n(A')) be?
#sets
#venn-diagrams
#complement-count
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A (16)
B (22)
C (38)
D (54)
Explanation opens after your attempt
Step 1
Concept
(n(A')=n(U)-n(A)=38-16=22). Complement is always found by subtracting from (U).
Step 2
Why this answer is correct
The correct answer is B. (22). (n(A')=n(U)-n(A)=38-16=22). Complement is always found by subtracting from (U).
Step 3
Exam Tip
(n(A')=n(U)-n(A)=38-16=22)। पूरक हमेशा (U) से घटाकर निकाला जाता है।
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यदि (n(A)=23) और (n\(A\cap B\)=9), तो केवल (A) में कितने अवयव होंगे?
If (n(A)=23) and (n\(A\cap B\)=9), how many elements will be only in (A)?
#sets
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#only-a
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A (9)
B (14)
C (23)
D (32)
Explanation opens after your attempt
Step 1
Concept
The number only in (A) is (23-9=14). Subtract the common part from total (A).
Step 2
Why this answer is correct
The correct answer is B. (14). The number only in (A) is (23-9=14). Subtract the common part from total (A).
Step 3
Exam Tip
केवल (A) की संख्या (23-9=14) है। (A) के कुल अवयवों से साझा भाग घटाएं।
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यदि (n(B)=27) और (n\(A\cap B\)=11), तो केवल (B) में कितने अवयव होंगे?
If (n(B)=27) and (n\(A\cap B\)=11), how many elements will be only in (B)?
#sets
#venn-diagrams
#only-b
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A (11)
B (16)
C (27)
D (38)
Explanation opens after your attempt
Step 1
Concept
The number only in (B) is (27-11=16). In the Venn diagram, subtract the middle part from circle (B).
Step 2
Why this answer is correct
The correct answer is B. (16). The number only in (B) is (27-11=16). In the Venn diagram, subtract the middle part from circle (B).
Step 3
Exam Tip
केवल (B) की संख्या (27-11=16) है। वेन आरेख में (B) वृत्त से बीच वाला भाग घटाएं।
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यदि केवल (A) में (12), \(A\cap B\) में (5), और केवल (B) में (8) अवयव हैं, तो (n\(A\cup B\)) क्या है?
If only (A) has (12), \(A\cap B\) has (5), and only (B) has (8) elements, what is (n\(A\cup B\))?
#sets
#venn-diagrams
#union-regions
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A (17)
B (20)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
The union contains all three regions, so (12+5+8=25). Add each separate region once in a Venn diagram.
Step 2
Why this answer is correct
The correct answer is C. (25). The union contains all three regions, so (12+5+8=25). Add each separate region once in a Venn diagram.
Step 3
Exam Tip
संघ में तीनों क्षेत्र आते हैं, इसलिए (12+5+8=25)। वेन आरेख में हर अलग क्षेत्र को एक बार जोड़ें।
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यदि (n(U)=52) और (n\(A\cup B\)=37), तो न (A) न (B) में कितने अवयव हैं?
If (n(U)=52) and (n\(A\cup B\)=37), how many elements are in neither (A) nor (B)?
#sets
#venn-diagrams
#neither
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A (15)
B (37)
C (52)
D (89)
Explanation opens after your attempt
Step 1
Concept
The number in neither (A) nor (B) is (52-37=15). It is the part inside (U) but outside both circles.
Step 2
Why this answer is correct
The correct answer is A. (15). The number in neither (A) nor (B) is (52-37=15). It is the part inside (U) but outside both circles.
Step 3
Exam Tip
न (A) न (B) की संख्या (52-37=15) है। यह (U) के अंदर दोनों वृत्तों के बाहर का भाग है।
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वेन आरेख में (A-B) कौन सा क्षेत्र है?
Which region is (A-B) in a Venn diagram?
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#set-difference
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A केवल (A) / Only (A)
B केवल (B) / Only (B)
C \(A\cap B\)
D पूरा (U) / Whole (U)
Explanation opens after your attempt
Correct Answer
A. केवल (A) / Only (A)
Step 1
Concept
(A-B) contains elements of (A) that are not in (B). So it is the only (A) region.
Step 2
Why this answer is correct
The correct answer is A. केवल (A) / Only (A). (A-B) contains elements of (A) that are not in (B). So it is the only (A) region.
Step 3
Exam Tip
(A-B) में (A) के वे अवयव होते हैं जो (B) में नहीं हैं। इसलिए यह केवल (A) वाला क्षेत्र है।
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वेन आरेख में (B-A) कौन सा क्षेत्र है?
Which region is (B-A) in a Venn diagram?
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A केवल (A) / Only (A)
B केवल (B) / Only (B)
C \(A\cup B\)
D \(A'\cap B'\)
Explanation opens after your attempt
Correct Answer
B. केवल (B) / Only (B)
Step 1
Concept
(B-A) contains elements of (B) that are not in (A). So it is the only (B) region.
Step 2
Why this answer is correct
The correct answer is B. केवल (B) / Only (B). (B-A) contains elements of (B) that are not in (A). So it is the only (B) region.
Step 3
Exam Tip
(B-A) में (B) के वे अवयव होते हैं जो (A) में नहीं हैं। इसलिए यह केवल (B) वाला क्षेत्र है।
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\(A\cap B'\) वेन आरेख में किस क्षेत्र को दिखाता है?
Which region does \(A\cap B'\) show in a Venn diagram?
#sets
#venn-diagrams
#complement
#only-a
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A केवल (A) / Only (A)
B केवल (B) / Only (B)
C दोनों (A) और (B) / Both (A) and (B)
D न (A) न (B) / Neither (A) nor (B)
Explanation opens after your attempt
Correct Answer
A. केवल (A) / Only (A)
Step 1
Concept
\(A\cap B'\) means being in (A) and not in (B). It is the only (A) region.
Step 2
Why this answer is correct
The correct answer is A. केवल (A) / Only (A). \(A\cap B'\) means being in (A) and not in (B). It is the only (A) region.
Step 3
Exam Tip
\(A\cap B'\) का अर्थ है (A) में होना और (B) में न होना। यह केवल (A) क्षेत्र है।
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डी मॉर्गन नियम के अनुसार (\(A\cup B\)') किसके बराबर है?
According to De Morgan's law, (\(A\cup B\)') is equal to what?
#sets
#venn-diagrams
#de-morgan
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A \(A'\cap B'\)
B \(A'\cup B'\)
C \(A\cap B\)
D (A-B)
Explanation opens after your attempt
Correct Answer
A. \(A'\cap B'\)
Step 1
Concept
By De Morgan's law, (\(A\cup B\)'=A'\cap B'). This rule helps in understanding the outside-both region.
Step 2
Why this answer is correct
The correct answer is A. \(A'\cap B'\). By De Morgan's law, (\(A\cup B\)'=A'\cap B'). This rule helps in understanding the outside-both region.
Step 3
Exam Tip
डी मॉर्गन नियम से (\(A\cup B\)'=A'\cap B')। दोनों के बाहर वाले क्षेत्र को समझने में यह नियम मदद करता है।
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डी मॉर्गन नियम के अनुसार (\(A\cap B\)') किसके बराबर है?
According to De Morgan's law, (\(A\cap B\)') is equal to what?
#sets
#venn-diagrams
#de-morgan
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A \(A'\cup B'\)
B \(A'\cap B'\)
C \(A\cup B\)
D (A-B)
Explanation opens after your attempt
Correct Answer
A. \(A'\cup B'\)
Step 1
Concept
By De Morgan's law, (\(A\cap B\)'=A'\cup B'). All regions except the common part are included in this complement.
Step 2
Why this answer is correct
The correct answer is A. \(A'\cup B'\). By De Morgan's law, (\(A\cap B\)'=A'\cup B'). All regions except the common part are included in this complement.
Step 3
Exam Tip
डी मॉर्गन नियम से (\(A\cap B\)'=A'\cup B')। साझा भाग को छोड़कर बाकी क्षेत्र इस पूरक में आते हैं।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{3,5,7\}\), तो \(A\cap B\) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{3,5,7\}\), what is \(A\cap B\)?
#sets
#venn-diagrams
#intersection-elements
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A ({1,2,4})
B ({3,5})
C ({7})
D ({1,2,3,4,5,7})
Explanation opens after your attempt
Correct Answer
B. ({3,5})
Step 1
Concept
The common elements in both sets are (3) and (5). Therefore, \(A\cap B={3,5}\).
Step 2
Why this answer is correct
The correct answer is B. ({3,5}). The common elements in both sets are (3) and (5). Therefore, \(A\cap B={3,5}\).
Step 3
Exam Tip
दोनों समुच्चयों में (3) और (5) समान हैं। इसलिए \(A\cap B={3,5}\)।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{1,2,8,9\}\), तो केवल (A) वाला भाग क्या है?
If \(A=\{2,4,6,8\}\) and \(B=\{1,2,8,9\}\), what is the only (A) part?
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#only-a-elements
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A ({4,6})
B ({2,8})
C ({1,9})
D ({2,4,6,8,1,9})
Explanation opens after your attempt
Correct Answer
A. ({4,6})
Step 1
Concept
For only (A), find (A-B). Since (2) and (8) are common, ({4,6}) remains.
Step 2
Why this answer is correct
The correct answer is A. ({4,6}). For only (A), find (A-B). Since (2) and (8) are common, ({4,6}) remains.
Step 3
Exam Tip
केवल (A) के लिए (A-B) निकालते हैं। (2) और (8) साझा हैं, इसलिए ({4,6}) बचता है।
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यदि \(A=\{a,c,e\}\) और \(B=\{b,c,d,e\}\), तो केवल (B) वाला भाग क्या है?
If \(A=\{a,c,e\}\) and \(B=\{b,c,d,e\}\), what is the only (B) part?
#sets
#venn-diagrams
#only-b-elements
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A ({c,e})
B ({a})
C ({b,d})
D ({a,b,c,d,e})
Explanation opens after your attempt
Correct Answer
C. ({b,d})
Step 1
Concept
For only (B), find (B-A). After removing (c) and (e), ({b,d}) remains.
Step 2
Why this answer is correct
The correct answer is C. ({b,d}). For only (B), find (B-A). After removing (c) and (e), ({b,d}) remains.
Step 3
Exam Tip
केवल (B) के लिए (B-A) निकालते हैं। (c) और (e) हटाने पर ({b,d}) बचता है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,4,6\}\), तो (A') क्या है?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,4,6\}\), what is (A')?
#sets
#venn-diagrams
#complement-elements
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A ({1,4,6})
B ({2,3,5})
C ({1,2,3,4,5,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({2,3,5})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). Therefore, (A'={2,3,5}).
Step 2
Why this answer is correct
The correct answer is B. ({2,3,5}). (A') contains the elements of (U) that are not in (A). Therefore, (A'={2,3,5}).
Step 3
Exam Tip
(A') में (U) के वे अवयव होंगे जो (A) में नहीं हैं। इसलिए (A'={2,3,5})।
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यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,b,d\}\), और \(B=\{b,c,d\}\), तो (\(A\cup B\)') क्या है?
If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,b,d\}\), and \(B=\{b,c,d\}\), what is (\(A\cup B\)')?
#sets
#venn-diagrams
#union-complement
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A ({e,f})
B ({a,c})
C ({b,d})
D ({a,b,c,d})
Explanation opens after your attempt
Correct Answer
A. ({e,f})
Step 1
Concept
\(A\cup B={a,b,c,d}\), so (\(A\cup B\)'={e,f}). First find the union and then take the complement.
Step 2
Why this answer is correct
The correct answer is A. ({e,f}). \(A\cup B={a,b,c,d}\), so (\(A\cup B\)'={e,f}). First find the union and then take the complement.
Step 3
Exam Tip
\(A\cup B={a,b,c,d}\), इसलिए (\(A\cup B\)'={e,f})। पहले संघ निकालें फिर पूरक लें।
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यदि (n(A-B)=10) और (n\(A\cap B\)=7), तो (n(A)) क्या है?
If (n(A-B)=10) and (n\(A\cap B\)=7), what is (n(A))?
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#region-addition
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A (3)
B (10)
C (17)
D (70)
Explanation opens after your attempt
Step 1
Concept
Set (A) contains only (A) and the common part. Therefore, (n(A)=10+7=17).
Step 2
Why this answer is correct
The correct answer is C. (17). Set (A) contains only (A) and the common part. Therefore, (n(A)=10+7=17).
Step 3
Exam Tip
(A) में केवल (A) और साझा भाग दोनों आते हैं। इसलिए (n(A)=10+7=17)।
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यदि (n(B-A)=13) और (n\(A\cap B\)=6), तो (n(B)) क्या है?
If (n(B-A)=13) and (n\(A\cap B\)=6), what is (n(B))?
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#region-addition
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A (7)
B (13)
C (19)
D (78)
Explanation opens after your attempt
Step 1
Concept
Set (B) contains only (B) and the common part. Therefore, (n(B)=13+6=19).
Step 2
Why this answer is correct
The correct answer is C. (19). Set (B) contains only (B) and the common part. Therefore, (n(B)=13+6=19).
Step 3
Exam Tip
(B) में केवल (B) और साझा भाग होते हैं। इसलिए (n(B)=13+6=19)।
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यदि (n(U)=64), केवल (A) में (18), \(A\cap B\) में (12), और केवल (B) में (20) हैं, तो बाहर का क्षेत्र कितना है?
If (n(U)=64), only (A) has (18), \(A\cap B\) has (12), and only (B) has (20), what is the outside region?
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#outside-region
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A (14)
B (30)
C (50)
D (64)
Explanation opens after your attempt
Step 1
Concept
The three known regions are (18+12+20=50). The outside region is (64-50=14).
Step 2
Why this answer is correct
The correct answer is A. (14). The three known regions are (18+12+20=50). The outside region is (64-50=14).
Step 3
Exam Tip
ज्ञात तीन क्षेत्र (18+12+20=50) हैं। बाहर का क्षेत्र (64-50=14) है।
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यदि (n(U)=80), बाहर (15), केवल (A) (25), और केवल (B) (18) है, तो (n\(A\cap B\)) क्या है?
If (n(U)=80), outside is (15), only (A) is (25), and only (B) is (18), what is (n\(A\cap B\))?
#sets
#venn-diagrams
#missing-region
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A (22)
B (37)
C (40)
D (58)
Explanation opens after your attempt
Step 1
Concept
The common part is (80-15-25-18=22). For an unknown region, subtract the other regions from (U).
Step 2
Why this answer is correct
The correct answer is A. (22). The common part is (80-15-25-18=22). For an unknown region, subtract the other regions from (U).
Step 3
Exam Tip
साझा भाग (80-15-25-18=22) है। अज्ञात क्षेत्र के लिए (U) से बाकी क्षेत्र घटाएं।
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यदि (n\(A\cup B\)=44), केवल (A) (16), और केवल (B) (19) है, तो (n\(A\cap B\)) क्या है?
If (n\(A\cup B\)=44), only (A) is (16), and only (B) is (19), what is (n\(A\cap B\))?
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#missing-intersection
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A (9)
B (16)
C (19)
D (35)
Explanation opens after your attempt
Step 1
Concept
The union contains only (A), the common part, and only (B). Therefore, the common part is (44-16-19=9).
Step 2
Why this answer is correct
The correct answer is A. (9). The union contains only (A), the common part, and only (B). Therefore, the common part is (44-16-19=9).
Step 3
Exam Tip
संघ में केवल (A), साझा भाग और केवल (B) आते हैं। इसलिए साझा भाग (44-16-19=9) है।
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किसी कक्षा में (42) विद्यार्थी हैं, (24) गणित पसंद करते हैं, (18) विज्ञान पसंद करते हैं, और (7) दोनों पसंद करते हैं। कम से कम एक विषय पसंद करने वाले कितने हैं?
In a class of (42) students, (24) like mathematics, (18) like science, and (7) like both. How many like at least one subject?
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#venn-diagrams
#word-problem
#union
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A (35)
B (42)
C (49)
D (7)
Explanation opens after your attempt
Step 1
Concept
Those who like at least one are (24+18-7=35). Do not count those who like both twice.
Step 2
Why this answer is correct
The correct answer is A. (35). Those who like at least one are (24+18-7=35). Do not count those who like both twice.
Step 3
Exam Tip
कम से कम एक पसंद करने वाले (24+18-7=35) हैं। दोनों पसंद करने वालों को दो बार न गिनें।
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एक सर्वे में (50) लोग हैं, (28) मोबाइल चलाते हैं, (20) कंप्यूटर चलाते हैं, और (10) दोनों चलाते हैं। कोई भी नहीं चलाने वाले कितने हैं?
In a survey of (50) people, (28) use a mobile, (20) use a computer, and (10) use both. How many use neither?
#sets
#venn-diagrams
#word-problem
#neither
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A (10)
B (12)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
Those who use at least one are (28+20-10=38). Those who use neither are (50-38=12).
Step 2
Why this answer is correct
The correct answer is B. (12). Those who use at least one are (28+20-10=38). Those who use neither are (50-38=12).
Step 3
Exam Tip
कम से कम एक चलाने वाले (28+20-10=38) हैं। कोई भी नहीं चलाने वाले (50-38=12) हैं।
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एक समूह में (36) लोग हैं, (17) चाय पीते हैं, (15) दूध पीते हैं, और (6) दोनों पीते हैं। केवल चाय पीने वाले कितने हैं?
In a group of (36) people, (17) drink tea, (15) drink milk, and (6) drink both. How many drink only tea?
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#venn-diagrams
#word-problem
#only-a
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A (6)
B (11)
C (15)
D (26)
Explanation opens after your attempt
Step 1
Concept
Those who drink only tea are (17-6=11). Subtract those who drink both from total tea drinkers.
Step 2
Why this answer is correct
The correct answer is B. (11). Those who drink only tea are (17-6=11). Subtract those who drink both from total tea drinkers.
Step 3
Exam Tip
केवल चाय पीने वाले (17-6=11) हैं। कुल चाय से दोनों पीने वालों को घटाएं।
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एक खेल शिविर में (55) विद्यार्थी हैं, (30) दौड़ में हैं, (22) तैराकी में हैं, और (8) दोनों में हैं। केवल तैराकी में कितने विद्यार्थी हैं?
In a sports camp of (55) students, (30) are in running, (22) are in swimming, and (8) are in both. How many students are only in swimming?
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#venn-diagrams
#word-problem
#only-b
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A (8)
B (14)
C (22)
D (44)
Explanation opens after your attempt
Step 1
Concept
Only swimming has (22-8=14) students. Subtract the common part from the second circle.
Step 2
Why this answer is correct
The correct answer is B. (14). Only swimming has (22-8=14) students. Subtract the common part from the second circle.
Step 3
Exam Tip
केवल तैराकी में (22-8=14) विद्यार्थी हैं। दूसरे वृत्त का साझा भाग घटाना होता है।
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यदि \(A\cap B=\varnothing\), (n(A)=15), और (n(B)=18), तो (n\(A\cup B\)) क्या है?
If \(A\cap B=\varnothing\), (n(A)=15), and (n(B)=18), what is (n\(A\cup B\))?
#sets
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#disjoint-count
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A (3)
B (15)
C (18)
D (33)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, the common part is (0). Therefore, (n\(A\cup B\)=15+18=33).
Step 2
Why this answer is correct
The correct answer is D. (33). For disjoint sets, the common part is (0). Therefore, (n\(A\cup B\)=15+18=33).
Step 3
Exam Tip
असंबद्ध समुच्चयों में साझा भाग (0) होता है। इसलिए (n\(A\cup B\)=15+18=33)।
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यदि \(A\subseteq B\), (n(A)=9), और (n(B)=26), तो (n\(A\cup B\)) क्या है?
If \(A\subseteq B\), (n(A)=9), and (n(B)=26), what is (n\(A\cup B\))?
#sets
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#subset-union
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A (9)
B (17)
C (26)
D (35)
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\), \(A\cup B=B\). Therefore, (n\(A\cup B\)=26).
Step 2
Why this answer is correct
The correct answer is C. (26). When \(A\subseteq B\), \(A\cup B=B\). Therefore, (n\(A\cup B\)=26).
Step 3
Exam Tip
\(A\subseteq B\) होने पर \(A\cup B=B\) होता है। इसलिए (n\(A\cup B\)=26)।
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यदि \(A\subseteq B\), (n(A)=12), और (n(B)=31), तो (n\(A\cap B\)) क्या है?
If \(A\subseteq B\), (n(A)=12), and (n(B)=31), what is (n\(A\cap B\))?
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#subset-intersection
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A (12)
B (19)
C (31)
D (43)
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\), \(A\cap B=A\). Therefore, (n\(A\cap B\)=12).
Step 2
Why this answer is correct
The correct answer is A. (12). When \(A\subseteq B\), \(A\cap B=A\). Therefore, (n\(A\cap B\)=12).
Step 3
Exam Tip
\(A\subseteq B\) होने पर \(A\cap B=A\) होता है। इसलिए (n\(A\cap B\)=12)।
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तीन समुच्चयों के वेन आरेख में बीच का सबसे सामान्य क्षेत्र किससे लिखा जाता है?
In a Venn diagram of three sets, how is the most central common region written?
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#venn-diagrams
#three-sets
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A \(A\cup B\cup C\)
B \(A\cap B\cap C\)
C (A-B)
D (C')
Explanation opens after your attempt
Correct Answer
B. \(A\cap B\cap C\)
Step 1
Concept
The central common region is shared by all three, so it is \(A\cap B\cap C\). In three-set diagrams, identify the center first.
Step 2
Why this answer is correct
The correct answer is B. \(A\cap B\cap C\). The central common region is shared by all three, so it is \(A\cap B\cap C\). In three-set diagrams, identify the center first.
Step 3
Exam Tip
बीच का सामान्य क्षेत्र तीनों में साझा होता है, इसलिए \(A\cap B\cap C\) है। तीन समुच्चयों में सबसे पहले केंद्र को पहचानें।
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यदि (n(A)=8), (n(B)=7), (n(C)=6), (n\(A\cap B\)=2), (n\(A\cap C\)=1), (n\(B\cap C\)=3), और (n\(A\cap B\cap C\)=1), तो (n\(A\cup B\cup C\)) क्या है?
If (n(A)=8), (n(B)=7), (n(C)=6), (n\(A\cap B\)=2), (n\(A\cap C\)=1), (n\(B\cap C\)=3), and (n\(A\cap B\cap C\)=1), what is (n\(A\cup B\cup C\))?
#sets
#venn-diagrams
#three-set-union
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A (16)
B (17)
C (21)
D (28)
Explanation opens after your attempt
Step 1
Concept
By the three-set formula, (8+7+6-2-1-3+1=16). Subtract pairwise intersections and add the common part of all three.
Step 2
Why this answer is correct
The correct answer is A. (16). By the three-set formula, (8+7+6-2-1-3+1=16). Subtract pairwise intersections and add the common part of all three.
Step 3
Exam Tip
तीन समुच्चयों के सूत्र से (8+7+6-2-1-3+1=16)। जोड़ी वाले प्रतिच्छेद घटाकर तीनों का साझा भाग जोड़ें।
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यदि (n(A)=11), (n(B)=9), और (n\(A\cap B\)=4), तो केवल (A) और केवल (B) की कुल संख्या क्या है?
If (n(A)=11), (n(B)=9), and (n\(A\cap B\)=4), what is the total number of only (A) and only (B)?
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#only-regions
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A (8)
B (12)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
Only (A=11-4=7) and only (B=9-4=5). Therefore, the total is (7+5=12).
Step 2
Why this answer is correct
The correct answer is B. (12). Only (A=11-4=7) and only (B=9-4=5). Therefore, the total is (7+5=12).
Step 3
Exam Tip
केवल (A=11-4=7) और केवल (B=9-4=5) है। इसलिए कुल (7+5=12)।
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यदि (n(A)=20), (n(B)=24), और केवल (A) में (13) अवयव हैं, तो (n\(A\cap B\)) क्या है?
If (n(A)=20), (n(B)=24), and only (A) has (13) elements, what is (n\(A\cap B\))?
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#missing-intersection
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A (7)
B (11)
C (13)
D (24)
Explanation opens after your attempt
Step 1
Concept
Out of total (20) elements of (A), only (A) has (13). Therefore, the common part is (20-13=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Out of total (20) elements of (A), only (A) has (13). Therefore, the common part is (20-13=7).
Step 3
Exam Tip
(A) के कुल (20) में केवल (A) (13) है। इसलिए साझा भाग (20-13=7) है।
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यदि (n(A)=28), (n(B)=30), और केवल (B) में (21) अवयव हैं, तो (n\(A\cap B\)) क्या है?
If (n(A)=28), (n(B)=30), and only (B) has (21) elements, what is (n\(A\cap B\))?
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#missing-intersection
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A (7)
B (9)
C (21)
D (30)
Explanation opens after your attempt
Step 1
Concept
Out of total (30) elements of (B), only (B) has (21). Therefore, the common part is (30-21=9).
Step 2
Why this answer is correct
The correct answer is B. (9). Out of total (30) elements of (B), only (B) has (21). Therefore, the common part is (30-21=9).
Step 3
Exam Tip
(B) के कुल (30) में केवल (B) (21) है। इसलिए साझा भाग (30-21=9) है।
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यदि (n(A)=17), (n(B)=12), और (n\(A\cap B\)=0), तो वेन आरेख में (A) और (B) कैसे हैं?
If (n(A)=17), (n(B)=12), and (n\(A\cap B\)=0), how are (A) and (B) in the Venn diagram?
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#venn-diagrams
#disjoint-concept
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A असंबद्ध / Disjoint
B समान / Equal
C उपसमुच्चय / Subset
D पूरक / Complement
Explanation opens after your attempt
Correct Answer
A. असंबद्ध / Disjoint
Step 1
Concept
(n\(A\cap B\)=0) means there is no common element. Therefore, (A) and (B) are disjoint.
Step 2
Why this answer is correct
The correct answer is A. असंबद्ध / Disjoint. (n\(A\cap B\)=0) means there is no common element. Therefore, (A) and (B) are disjoint.
Step 3
Exam Tip
(n\(A\cap B\)=0) का अर्थ है कोई साझा अवयव नहीं। इसलिए (A) और (B) असंबद्ध हैं।
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यदि (A=B), तो वेन आरेख में \(A\cap B\) किसके बराबर होगा?
If (A=B), then in a Venn diagram, \(A\cap B\) will be equal to what?
#sets
#venn-diagrams
#equal-sets
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A (A)
B \(\varnothing\)
C (U)
D (A')
Explanation opens after your attempt
Step 1
Concept
When (A=B), both circles are exactly the same. Therefore, \(A\cap B=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). When (A=B), both circles are exactly the same. Therefore, \(A\cap B=A\).
Step 3
Exam Tip
जब (A=B), तब दोनों वृत्त पूरी तरह एक जैसे हैं। इसलिए \(A\cap B=A\) होता है।
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यदि (A=B), तो वेन आरेख में \(A\cup B\) किसके बराबर होगा?
If (A=B), then in a Venn diagram, \(A\cup B\) will be equal to what?
#sets
#venn-diagrams
#equal-sets-union
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A (A)
B \(\varnothing\)
C (A')
D (U-A)
Explanation opens after your attempt
Step 1
Concept
When (A=B), their union is the same set. Therefore, \(A\cup B=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). When (A=B), their union is the same set. Therefore, \(A\cup B=A\).
Step 3
Exam Tip
जब (A=B), तब दोनों का संघ वही समुच्चय होता है। इसलिए \(A\cup B=A\) है।
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कौन सा कथन हमेशा सही है?
Which statement is always correct?
#sets
#venn-diagrams
#true-statement
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A \(A\cap B\subseteq A\)
B \(A\cup B\subseteq A\cap B\)
C (A-B=B-A)
D (A'=A)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B\subseteq A\)
Step 1
Concept
All elements of \(A\cap B\) must be in (A). Therefore, \(A\cap B\subseteq A\) is always correct.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B\subseteq A\). All elements of \(A\cap B\) must be in (A). Therefore, \(A\cap B\subseteq A\) is always correct.
Step 3
Exam Tip
\(A\cap B\) के सभी अवयव (A) में जरूर होते हैं। इसलिए \(A\cap B\subseteq A\) हमेशा सही है।
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वेन आरेख में \(A\cup A'\) किसके बराबर होता है?
In a Venn diagram, \(A\cup A'\) is equal to what?
#sets
#venn-diagrams
#complement-law
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A (A)
B (A')
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(A) and (A') together make the whole (U). Therefore, \(A\cup A'=U\).
Step 2
Why this answer is correct
The correct answer is C. (U). (A) and (A') together make the whole (U). Therefore, \(A\cup A'=U\).
Step 3
Exam Tip
(A) और (A') मिलकर पूरा (U) बनाते हैं। इसलिए \(A\cup A'=U\)।
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वेन आरेख में \(A\cap A'\) किसके बराबर होता है?
In a Venn diagram, \(A\cap A'\) is equal to what?
#sets
#venn-diagrams
#complement-law
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A (A)
B (U)
C \(\varnothing\)
D (A')
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\)
Step 1
Concept
No element can be in both (A) and (A') at the same time. Therefore, \(A\cap A'=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \(\varnothing\). No element can be in both (A) and (A') at the same time. Therefore, \(A\cap A'=\varnothing\).
Step 3
Exam Tip
कोई भी अवयव (A) और (A') दोनों में साथ-साथ नहीं हो सकता। इसलिए \(A\cap A'=\varnothing\)।
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यदि (n(U)=100), (n(A)=45), (n(B)=40), और (n\(A\cap B\)=15), तो (n(\(A\cup B\)')) क्या है?
If (n(U)=100), (n(A)=45), (n(B)=40), and (n\(A\cap B\)=15), what is (n(\(A\cup B\)'))?
#sets
#venn-diagrams
#union-complement-count
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A (30)
B (40)
C (70)
D (85)
Explanation opens after your attempt
Step 1
Concept
First, (n\(A\cup B\)=45+40-15=70). Therefore, (n(\(A\cup B\)')=100-70=30).
Step 2
Why this answer is correct
The correct answer is A. (30). First, (n\(A\cup B\)=45+40-15=70). Therefore, (n(\(A\cup B\)')=100-70=30).
Step 3
Exam Tip
पहले (n\(A\cup B\)=45+40-15=70)। इसलिए (n(\(A\cup B\)')=100-70=30)।
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यदि (n(U)=90), (n\(A\cap B\)=25), तो (n(\(A\cap B\)')) क्या है?
If (n(U)=90) and (n\(A\cap B\)=25), what is (n(\(A\cap B\)'))?
#sets
#venn-diagrams
#intersection-complement-count
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A (25)
B (65)
C (90)
D (115)
Explanation opens after your attempt
Step 1
Concept
(\(A\cap B\)') contains all elements of (U) except the common part. Therefore, the number is (90-25=65).
Step 2
Why this answer is correct
The correct answer is B. (65). (\(A\cap B\)') contains all elements of (U) except the common part. Therefore, the number is (90-25=65).
Step 3
Exam Tip
(\(A\cap B\)') में साझा भाग को छोड़कर (U) के बाकी अवयव आते हैं। इसलिए संख्या (90-25=65) है।
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यदि (n(A)=32), (n\(A\cup B\)=48), और (n\(A\cap B\)=10), तो (n(B)) क्या है?
If (n(A)=32), (n\(A\cup B\)=48), and (n\(A\cap B\)=10), what is (n(B))?
#sets
#venn-diagrams
#unknown-cardinality
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A (16)
B (26)
C (38)
D (58)
Explanation opens after your attempt
Step 1
Concept
From (48=32+n(B)-10), we get (n(B)=26). Isolate the unknown in the union formula.
Step 2
Why this answer is correct
The correct answer is B. (26). From (48=32+n(B)-10), we get (n(B)=26). Isolate the unknown in the union formula.
Step 3
Exam Tip
सूत्र (48=32+n(B)-10) से (n(B)=26) मिलता है। संघ के सूत्र में अज्ञात को अलग करें।
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