यदि \(A=\{2,4,6,8,10\}\), \(B=\{1,2,3,4,5\}\) और \(C=\{4,5,6,7\}\) है, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{2,4,6,8,10\}\), \(B=\{1,2,3,4,5\}\), and \(C=\{4,5,6,7\}\), what is (A\cap\(B\cup C\))?
#sets
#mixed-operations
#union-intersection
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A ( {2,4,6} )
B ( {4,6} )
C ( {1,2,3,4,5,6,7} )
D ( {8,10} )
Explanation opens after your attempt
Correct Answer
A. ( {2,4,6} )
Step 1
Concept
First \(B\cup C={1,2,3,4,5,6,7}\). Its intersection with (A) is ({2,4,6}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,4,6} ). First \(B\cup C={1,2,3,4,5,6,7}\). Its intersection with (A) is ({2,4,6}).
Step 3
Exam Tip
पहले \(B\cup C={1,2,3,4,5,6,7}\) है। इसका (A) से प्रतिच्छेद ({2,4,6}) है।
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\(यदि (A={x:x\in \mathbb{N}, 1\le x\le 30, x\) का गुणज 2 है\(}) और (B={x:x\in \mathbb{N}, 1\le x\le 30, x\) का गुणज 3 है\(}), तो (A\cap B) में कितने अवयव हैं\)?
\(If (A={x:x\in \mathbb{N}, 1\le x\le 30, x\) is a multiple of \(2}) and (B={x:x\in \mathbb{N}, 1\le x\le 30, x\) is a multiple of \(3}), how many elements are in (A\cap B)\)?
#sets
#multiples
#intersection
#cardinality
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A (5)
B (10)
C (15)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B\) contains multiples of both (2) and (3), that is, multiples of (6). Up to (30), these elements are ({6,12,18,24,30}).
Step 2
Why this answer is correct
The correct answer is A. (5). \(A\cap B\) contains multiples of both (2) and (3), that is, multiples of (6). Up to (30), these elements are ({6,12,18,24,30}).
Step 3
Exam Tip
\(A\cap B\) में (2) और (3) दोनों के गुणज, यानी (6) के गुणज आएंगे। (30) तक ऐसे अवयव ({6,12,18,24,30}) हैं।
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यदि \(P=\{a,b,c,d\}\) और \(Q=\{b,d,e\}\) है, तो \(P\cap Q\) ज्ञात कीजिए।
If \(P=\{a,b,c,d\}\) and \(Q=\{b,d,e\}\), find \(P\cap Q\).
#sets
#intersection
#common-elements
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A ( {a,c,e} )
B ( {b,d} )
C ( {a,b,c,d,e} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {b,d} )
Step 1
Concept
\(P\cap Q\) contains only elements common to both sets. Finding common elements should be the first step.
Step 2
Why this answer is correct
The correct answer is B. ( {b,d} ). \(P\cap Q\) contains only elements common to both sets. Finding common elements should be the first step.
Step 3
Exam Tip
\(P\cap Q\) में केवल वे अवयव आते हैं जो दोनों में समान हों। समान अवयव ढूंढना सबसे पहला कदम रखें।
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\(यदि (A={x:x\in \mathbb{N}, x\le 15}) और (B={x:x\in \mathbb{N}, x\) विषम है\(, x\le 15}) है, तो (A-B) क्या है\)?
\(If (A={x:x\in \mathbb{N}, x\le 15}) and (B={x:x\in \mathbb{N}, x\) is odd\(, x\le 15}), what is (A-B)\)?
#sets
#natural-numbers
#difference
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A ( {1,3,5,7,9,11,13,15} )
B ( {2,4,6,8,10,12,14} )
C ( {2,4,6,8,10,12,14,16} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {2,4,6,8,10,12,14} )
Step 1
Concept
(A-B) keeps elements of (A) that are not in (B). So the even numbers up to (15) are the answer.
Step 2
Why this answer is correct
The correct answer is B. ( {2,4,6,8,10,12,14} ). (A-B) keeps elements of (A) that are not in (B). So the even numbers up to (15) are the answer.
Step 3
Exam Tip
(A-B) में (A) के वे अवयव रहेंगे जो (B) में नहीं हैं। इसलिए (15) तक की सम संख्याएं उत्तर हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,7\}\) और \(B=\{2,4,5,8,10\}\) है, तो (\(A\cap B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,7\}\), and \(B=\{2,4,5,8,10\}\), what is (\(A\cap B\)')?
#sets
#complement
#intersection
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A ( {2,5} )
B ( {1,3,4,6,7,8,9,10} )
C ( {1,2,4,5,7,8,10} )
D ( {3,6,9} )
Explanation opens after your attempt
Correct Answer
B. ( {1,3,4,6,7,8,9,10} )
Step 1
Concept
First \(A\cap B={2,5}\). The elements outside it in (U) are ({1,3,4,6,7,8,9,10}).
Step 2
Why this answer is correct
The correct answer is B. ( {1,3,4,6,7,8,9,10} ). First \(A\cap B={2,5}\). The elements outside it in (U) are ({1,3,4,6,7,8,9,10}).
Step 3
Exam Tip
पहले \(A\cap B={2,5}\) है। (U) में इसके बाहर के अवयव ({1,3,4,6,7,8,9,10}) हैं।
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यदि (n(A)=35), (n(B)=27) और (n\(A\cup B\)=50), तो (n(A-B)) क्या है?
If (n(A)=35), (n(B)=27), and (n\(A\cup B\)=50), what is (n(A-B))?
#sets
#cardinality
#difference
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A (8)
B (12)
C (23)
D (15)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cap B\)=35+27-50=12). Therefore (n(A-B)=35-12=23).
Step 2
Why this answer is correct
The correct answer is C. (23). First (n\(A\cap B\)=35+27-50=12). Therefore (n(A-B)=35-12=23).
Step 3
Exam Tip
पहले (n\(A\cap B\)=35+27-50=12) है। इसलिए (n(A-B)=35-12=23)।
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एक समूह में (24) विद्यार्थी हिंदी, (18) विद्यार्थी अंग्रेजी और (7) विद्यार्थी दोनों पढ़ते हैं। केवल हिंदी पढ़ने वाले विद्यार्थियों की संख्या क्या है?
In a group, (24) students study Hindi, (18) students study English, and (7) students study both. How many students study only Hindi?
#sets
#word-problem
#difference
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A (17)
B (35)
C (31)
D (11)
Explanation opens after your attempt
Step 1
Concept
Only Hindi means (H-E). The number is (24-7=17).
Step 2
Why this answer is correct
The correct answer is A. (17). Only Hindi means (H-E). The number is (24-7=17).
Step 3
Exam Tip
केवल हिंदी का अर्थ (H-E) है। संख्या (24-7=17) होगी।
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यदि \(A=\{2,4,6,8,10\}\) और \(B=\{1,2,3,4\}\) है, तो (B-A) क्या है?
If \(A=\{2,4,6,8,10\}\) and \(B=\{1,2,3,4\}\), what is (B-A)?
#sets
#difference
#order
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A ( {1,3} )
B ( {6,8,10} )
C ( {2,4} )
D ( {1,2,3,4,6,8,10} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3} )
Step 1
Concept
In (B-A), common elements with (A) are removed from (B). So (1) and (3) remain.
Step 2
Why this answer is correct
The correct answer is A. ( {1,3} ). In (B-A), common elements with (A) are removed from (B). So (1) and (3) remain.
Step 3
Exam Tip
(B-A) में (B) से (A) के सामान्य अवयव हटा दिए जाते हैं। इसलिए (1) और (3) बचते हैं।
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यदि (A=[-1,4]) और (B=(1,6)), तो \(A\cap B\) क्या है?
If (A=[-1,4]) and (B=(1,6)), what is \(A\cap B\)?
#sets
#intervals
#intersection
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A ( [-1,6) )
B ( (1,4] )
C ( [1,4] )
D ( (-1,1] )
Explanation opens after your attempt
Correct Answer
B. ( (1,4] )
Step 1
Concept
The common part of both intervals is from (1) to (4). Since (1) is not included and (4) is included, ((1,4]) is correct.
Step 2
Why this answer is correct
The correct answer is B. ( (1,4] ). The common part of both intervals is from (1) to (4). Since (1) is not included and (4) is included, ((1,4]) is correct.
Step 3
Exam Tip
दोनों अंतरालों का सामान्य भाग (1) से (4) तक है। (1) शामिल नहीं और (4) शामिल है, इसलिए ((1,4]) सही है।
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यदि \(A={x:x^2-7x+12=0}\) और \(B={x:x^2-9x+20=0}\), तो \(A\cup B\) क्या है?
If \(A={x:x^2-7x+12=0}\) and \(B={x:x^2-9x+20=0}\), what is \(A\cup B\)?
#sets
#quadratic
#union
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A ( {3,4,5} )
B ( {3,4} )
C ( {4,5} )
D ( {3,5} )
Explanation opens after your attempt
Correct Answer
A. ( {3,4,5} )
Step 1
Concept
\(A=\{3,4\}\) and \(B=\{4,5\}\). In a union, the repeated element (4) is written only once.
Step 2
Why this answer is correct
The correct answer is A. ( {3,4,5} ). \(A=\{3,4\}\) and \(B=\{4,5\}\). In a union, the repeated element (4) is written only once.
Step 3
Exam Tip
\(A=\{3,4\}\) और \(B=\{4,5\}\) है। संघ में दोहराया अवयव (4) केवल एक बार लिखा जाता है।
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यदि \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\) और \(C=\{4,5,6\}\) है, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{3,4,5\}\), and \(C=\{4,5,6\}\), what is (\(A\cup B\)\cap C)?
#sets
#mixed-operations
#intersection
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A ( {4,5} )
B ( {3,4} )
C ( {1,2,3,4,5,6} )
D ( {5,6} )
Explanation opens after your attempt
Correct Answer
A. ( {4,5} )
Step 1
Concept
First \(A\cup B={1,2,3,4,5}\). Its common part with (C) is ({4,5}).
Step 2
Why this answer is correct
The correct answer is A. ( {4,5} ). First \(A\cup B={1,2,3,4,5}\). Its common part with (C) is ({4,5}).
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,4,5}\) है। इसका (C) से सामान्य भाग ({4,5}) है।
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यदि \(A=\{1,4,9,16,25\}\) और \(B=\{2,4,8,16,32\}\), तो \((A-B)\cup(B-A)\) क्या है?
If \(A=\{1,4,9,16,25\}\) and \(B=\{2,4,8,16,32\}\), what is \((A-B)\cup(B-A)\)?
#sets
#symmetric-difference
#application
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A ( {4,16} )
B ( {1,2,8,9,25,32} )
C ( {1,4,9,16,25,2,8,32} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {1,2,8,9,25,32} )
Step 1
Concept
(A-B={1,9,25}) and (B-A={2,8,32}). Their union is ({1,2,8,9,25,32}).
Step 2
Why this answer is correct
The correct answer is B. ( {1,2,8,9,25,32} ). (A-B={1,9,25}) and (B-A={2,8,32}). Their union is ({1,2,8,9,25,32}).
Step 3
Exam Tip
(A-B={1,9,25}) और (B-A={2,8,32}) है। दोनों का संघ ({1,2,8,9,25,32}) है।
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यदि \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8\}\) और \(C=\{3,4,5,6\}\) है, तो (A-\(B\cap C\)) क्या है?
If \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8\}\), and \(C=\{3,4,5,6\}\), what is (A-\(B\cap C\))?
#sets
#difference
#compound
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A ( {1,7,9} )
B ( {3,5} )
C ( {1,3,5,7,9} )
D ( {2,4,6,8} )
Explanation opens after your attempt
Correct Answer
A. ( {1,7,9} )
Step 1
Concept
\(B\cap C={3,5}\). Removing these from (A) gives ({1,7,9}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,7,9} ). \(B\cap C={3,5}\). Removing these from (A) gives ({1,7,9}).
Step 3
Exam Tip
\(B\cap C={3,5}\) है। इन्हें (A) से हटाने पर ({1,7,9}) मिलता है।
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यदि (n(A)=18), (n(B)=14) और (n\(A\cap B\)=6), तो (n\(A\cup B\)) क्या है?
If (n(A)=18), (n(B)=14), and (n\(A\cap B\)=6), what is (n\(A\cup B\))?
#sets
#cardinality
#union-formula
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A (26)
B (32)
C (38)
D (20)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (18+14-6=26).
Step 2
Why this answer is correct
The correct answer is A. (26). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (18+14-6=26).
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाइए। इसलिए (18+14-6=26)।
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यदि (n\(A\cup B\)=45), (n(A)=28) और (n(B)=25), तो (n\(A\cap B\)) ज्ञात कीजिए।
If (n\(A\cup B\)=45), (n(A)=28), and (n(B)=25), find (n\(A\cap B\)).
#sets
#cardinality
#intersection
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A (8)
B (12)
C (17)
D (53)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)). Therefore (28+25-45=8).
Step 2
Why this answer is correct
The correct answer is A. (8). (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)). Therefore (28+25-45=8).
Step 3
Exam Tip
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)) है। इसलिए (28+25-45=8)।
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एक कक्षा में (30) विद्यार्थी गणित, (22) विद्यार्थी भौतिकी और (12) विद्यार्थी दोनों पढ़ते हैं। कम से कम एक विषय पढ़ने वाले विद्यार्थियों की संख्या क्या है?
In a class, (30) students study Mathematics, (22) students study Physics, and (12) students study both. How many students study at least one subject?
#sets
#word-problem
#union
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A (40)
B (52)
C (64)
D (20)
Explanation opens after your attempt
Step 1
Concept
At least one means \(M\cup P\). The number is (30+22-12=40).
Step 2
Why this answer is correct
The correct answer is A. (40). At least one means \(M\cup P\). The number is (30+22-12=40).
Step 3
Exam Tip
कम से कम एक का अर्थ \(M\cup P\) है। संख्या (30+22-12=40) होगी।
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\(यदि (A={x:x\in \mathbb{Z}, -2\le x\le 4}) और (B={x:x\in \mathbb{Z}, x\) विषम है\(}) है, तो (A\cap B) क्या है\)?
\(If (A={x:x\in \mathbb{Z}, -2\le x\le 4}) and (B={x:x\in \mathbb{Z}, x\) is odd\(}), what is (A\cap B)\)?
#sets
#set-builder
#integers
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A ( {-1,1,3} )
B ( {-2,0,2,4} )
C ( {-2,-1,0,1,2,3,4} )
D ( {1,3,5} )
Explanation opens after your attempt
Correct Answer
A. ( {-1,1,3} )
Step 1
Concept
(A) contains integers from (-2) to (4). The odd integers among them are (-1,1,3).
Step 2
Why this answer is correct
The correct answer is A. ( {-1,1,3} ). (A) contains integers from (-2) to (4). The odd integers among them are (-1,1,3).
Step 3
Exam Tip
(A) में (-2) से (4) तक के पूर्णांक हैं। इनमें विषम पूर्णांक (-1,1,3) हैं।
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यदि (A=[1,5]) और (B=[3,8]), तो \(A\cap B\) कौन-सा अंतराल है?
If (A=[1,5]) and (B=[3,8]), which interval is \(A\cap B\)?
#sets
#intervals
#intersection
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A ( [1,8] )
B ( [3,5] )
C ( [1,3] )
D ( [5,8] )
Explanation opens after your attempt
Correct Answer
B. ( [3,5] )
Step 1
Concept
The common part of both intervals is from (3) to (5). Keep closed endpoints carefully.
Step 2
Why this answer is correct
The correct answer is B. ( [3,5] ). The common part of both intervals is from (3) to (5). Keep closed endpoints carefully.
Step 3
Exam Tip
दोनों अंतरालों में सामान्य भाग (3) से (5) तक है। बंद सिरों को ध्यान से रखें।
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यदि (A=(2,7)) और (B=[5,9]), तो \(A\cup B\) क्या होगा?
If (A=(2,7)) and (B=[5,9]), what is \(A\cup B\)?
#sets
#intervals
#union
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A ( (2,9] )
B ( [2,9] )
C ( [5,7) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (2,9] )
Step 1
Concept
The intervals overlap between (5) and (7). Since (2) is not included and (9) is included, ((2,9]) is correct.
Step 2
Why this answer is correct
The correct answer is A. ( (2,9] ). The intervals overlap between (5) and (7). Since (2) is not included and (9) is included, ((2,9]) is correct.
Step 3
Exam Tip
दोनों अंतराल (5) से (7) के बीच जुड़ते हैं। (2) शामिल नहीं और (9) शामिल है, इसलिए ((2,9]) सही है।
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यदि (A=[0,6]) और (B=(2,4)), तो (A-B) क्या है?
If (A=[0,6]) and (B=(2,4)), what is (A-B)?
#sets
#intervals
#difference
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A \( [0,2]\cup[4,6] \)
B ( [0,2)\cup(4,6] )
C ( (2,4) )
D ( [2,4] )
Explanation opens after your attempt
Correct Answer
A. \( [0,2]\cup[4,6] \)
Step 1
Concept
(B=(2,4)) does not include (2) and (4). So (2) and (4) remain in (A-B).
Step 2
Why this answer is correct
The correct answer is A. \( [0,2]\cup[4,6] \). (B=(2,4)) does not include (2) and (4). So (2) and (4) remain in (A-B).
Step 3
Exam Tip
(B=(2,4)) में (2) और (4) शामिल नहीं हैं। इसलिए (A-B) में (2) और (4) रहेंगे।
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यदि \(A={x:x^2=9}\) और \(B={x:x^2-4=0}\), तो \(A\cup B\) क्या है?
If \(A={x:x^2=9}\) and \(B={x:x^2-4=0}\), what is \(A\cup B\)?
#sets
#equations
#union
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A ( {-3,3,-2,2} )
B ( {-3,3} )
C ( {-2,2} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {-3,3,-2,2} )
Step 1
Concept
\(A=\{-3,3\}\) and \(B=\{-2,2\}\). The union contains all elements from both sets.
Step 2
Why this answer is correct
The correct answer is A. ( {-3,3,-2,2} ). \(A=\{-3,3\}\) and \(B=\{-2,2\}\). The union contains all elements from both sets.
Step 3
Exam Tip
\(A=\{-3,3\}\) और \(B=\{-2,2\}\) है। संघ में दोनों के सभी अवयव आते हैं।
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यदि \(A={x:x^2-5x+6=0}\) और \(B={x:x^2-3x+2=0}\), तो \(A\cap B\) क्या होगा?
If \(A={x:x^2-5x+6=0}\) and \(B={x:x^2-3x+2=0}\), what is \(A\cap B\)?
#sets
#quadratic
#intersection
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A ( {1,2,3} )
B ( {2} )
C ( {3} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {2} )
Step 1
Concept
First get \(A=\{2,3\}\) and \(B=\{1,2\}\). The only common element is (2).
Step 2
Why this answer is correct
The correct answer is B. ( {2} ). First get \(A=\{2,3\}\) and \(B=\{1,2\}\). The only common element is (2).
Step 3
Exam Tip
पहले \(A=\{2,3\}\) और \(B=\{1,2\}\) निकालें। दोनों में समान अवयव केवल (2) है।
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किस विकल्प में (A-\(A\cap B\)) के बराबर समुच्चय दिया है?
Which option gives a set equal to (A-\(A\cap B\))?
#sets
#identity
#difference
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A (A-B)
B \(A\cup B\)
C (B-A)
D \(A\cap B\)
Explanation opens after your attempt
Step 1
Concept
Removing \(A\cap B\) from (A) leaves the part of (A) outside (B). This is (A-B).
Step 2
Why this answer is correct
The correct answer is A. (A-B). Removing \(A\cap B\) from (A) leaves the part of (A) outside (B). This is (A-B).
Step 3
Exam Tip
\(A\cap B\) को (A) से हटाने पर (A) का केवल (B) से बाहर वाला भाग बचता है। यही (A-B) है।
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कौन-सा नियम (A\cap\(B\cup C\)) के बराबर है?
Which law gives an expression equal to (A\cap\(B\cup C\))?
#sets
#distributive-law
#identity
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A ( \(A\cap B\)\cup\(A\cap C\) )
B ( \(A\cup B\)\cap\(A\cup C\) )
C \((A-B)\cup C\)
D ( A\cup\(B\cap C\) )
Explanation opens after your attempt
Correct Answer
A. ( \(A\cap B\)\cup\(A\cap C\) )
Step 1
Concept
This is the distributive law of intersection over union. Remembering the formula reduces mistakes in mixed operations.
Step 2
Why this answer is correct
The correct answer is A. ( \(A\cap B\)\cup\(A\cap C\) ). This is the distributive law of intersection over union. Remembering the formula reduces mistakes in mixed operations.
Step 3
Exam Tip
यह प्रतिच्छेद का संघ पर वितरण नियम है। सूत्र याद रखने से मिश्रित क्रियाओं में गलती कम होती है।
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कौन-सा व्यंजक (\(A\cup B\)-A) के बराबर है?
Which expression is equal to (\(A\cup B\)-A)?
#sets
#set-difference
#identity
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A (A-B)
B (B-A)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Step 1
Concept
Removing (A) from \(A\cup B\) leaves the part of (B) not in (A). Therefore the answer is (B-A).
Step 2
Why this answer is correct
The correct answer is B. (B-A). Removing (A) from \(A\cup B\) leaves the part of (B) not in (A). Therefore the answer is (B-A).
Step 3
Exam Tip
\(A\cup B\) से (A) हटाने पर (B) का वह भाग बचता है जो (A) में नहीं है। इसलिए उत्तर (B-A) है।
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यदि \(A=\{1,2,3\}\) और \(B=\{4,5\}\), तो \(A\cap B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{4,5\}\), what is \(A\cap B\)?
#sets
#disjoint
#intersection
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A ( {1,2,3,4,5} )
B ( {1,4} )
C \( \varnothing \)
D ( {3,4} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
There is no common element in the two sets. Such sets are disjoint and their intersection is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). There is no common element in the two sets. Such sets are disjoint and their intersection is \(\varnothing\).
Step 3
Exam Tip
दोनों समुच्चयों में कोई समान अवयव नहीं है। ऐसे समुच्चय असंयुक्त होते हैं और प्रतिच्छेद \(\varnothing\) होता है।
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यदि \(A\cap B=\varnothing\), (n(A)=9) और (n(B)=11), तो (n\(A\cup B\)) क्या होगा?
If \(A\cap B=\varnothing\), (n(A)=9), and (n(B)=11), what is (n\(A\cup B\))?
#sets
#disjoint
#cardinality
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A (2)
B (20)
C (99)
D (11)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, (n\(A\cap B\)=0). Hence (n\(A\cup B\)=9+11=20).
Step 2
Why this answer is correct
The correct answer is B. (20). For disjoint sets, (n\(A\cap B\)=0). Hence (n\(A\cup B\)=9+11=20).
Step 3
Exam Tip
असंयुक्त समुच्चयों में (n\(A\cap B\)=0) होता है। इसलिए (n\(A\cup B\)=9+11=20)।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\), तो \(A'\cap B\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{2,4,6,8\}\), and \(B=\{1,2,3,4\}\), what is \(A'\cap B\)?
#sets
#complement
#intersection
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A ( {1,3} )
B ( {2,4} )
C ( {5,7,9} )
D ( {1,2,3,4} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3} )
Step 1
Concept
(A'={1,3,5,7,9}). Its common part with (B) is ({1,3}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3} ). (A'={1,3,5,7,9}). Its common part with (B) is ({1,3}).
Step 3
Exam Tip
(A'={1,3,5,7,9}) है। इसका (B) से सामान्य भाग ({1,3}) है।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4,6\}\), तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4,6\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#symmetric-difference
#compound
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A ( {2,4} )
B ( {1,3,5,6} )
C ( {1,2,3,4,5,6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
B. ( {1,3,5,6} )
Step 1
Concept
\(A\cup B={1,2,3,4,5,6}\) and \(A\cap B={2,4}\). Taking the difference gives ({1,3,5,6}).
Step 2
Why this answer is correct
The correct answer is B. ( {1,3,5,6} ). \(A\cup B={1,2,3,4,5,6}\) and \(A\cap B={2,4}\). Taking the difference gives ({1,3,5,6}).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6}\) और \(A\cap B={2,4}\) है। अंतर लेने पर ({1,3,5,6}) मिलता है।
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यदि (A-B={1,5}), (B-A={7}) और \(A\cap B={2,3}\), तो \(A\cup B\) क्या होगा?
If (A-B={1,5}), (B-A={7}), and \(A\cap B={2,3}\), what is \(A\cup B\)?
#sets
#venn-parts
#union
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A ( {1,2,3,5,7} )
B ( {1,5,7} )
C ( {2,3} )
D ( {1,2,5} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,5,7} )
Step 1
Concept
The union contains all parts (A-B), (B-A), and \(A\cap B\). Combining them gives ({1,2,3,5,7}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,5,7} ). The union contains all parts (A-B), (B-A), and \(A\cap B\). Combining them gives ({1,2,3,5,7}).
Step 3
Exam Tip
संघ में (A-B), (B-A) और \(A\cap B\) के सभी भाग आते हैं। इन्हें मिलाने पर ({1,2,3,5,7}) मिलता है।
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यदि (n(A-B)=13) और (n\(A\cap B\)=7), तो (n(A)) क्या है?
If (n(A-B)=13) and (n\(A\cap B\)=7), what is (n(A))?
#sets
#cardinality
#difference
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A (6)
B (20)
C (91)
D (13)
Explanation opens after your attempt
Step 1
Concept
(A) is made of two disjoint parts (A-B) and \(A\cap B\). Hence (n(A)=13+7=20).
Step 2
Why this answer is correct
The correct answer is B. (20). (A) is made of two disjoint parts (A-B) and \(A\cap B\). Hence (n(A)=13+7=20).
Step 3
Exam Tip
(A) दो अलग भागों (A-B) और \(A\cap B\) से बनता है। इसलिए (n(A)=13+7=20)।
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\(यदि (A={x:x\) अंग्रेजी वर्णमाला का स्वर है\(}) और (B={a,b,c,d,e}), तो (A\cap B) क्या है\)?
\(If (A={x:x\) is a vowel in the English alphabet\(}) and (B={a,b,c,d,e}), what is (A\cap B)\)?
#sets
#application
#intersection
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A ( {a,e} )
B ( {b,c,d} )
C ( {a,b,c,d,e} )
D ( {i,o,u} )
Explanation opens after your attempt
Correct Answer
A. ( {a,e} )
Step 1
Concept
English vowels are (a,e,i,o,u). Among these, (a) and (e) are present in (B).
Step 2
Why this answer is correct
The correct answer is A. ( {a,e} ). English vowels are (a,e,i,o,u). Among these, (a) and (e) are present in (B).
Step 3
Exam Tip
अंग्रेजी स्वरों में (a,e,i,o,u) होते हैं। (B) में इनमें से (a) और (e) मौजूद हैं।
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\(यदि (A={x:x\) अभाज्य संख्या है\(, x<15}) और (B={x:x\) विषम संख्या है\(, x<15}), तो (A-B) क्या है\)?
\(If (A={x:x\) is a prime number\(, x<15}) and (B={x:x\) is an odd number\(, x<15}), what is (A-B)\)?
#sets
#prime-numbers
#difference
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A ( {2} )
B ( {3,5,7,11,13} )
C ( {2,3,5,7,11,13} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {2} )
Step 1
Concept
\(A=\{2,3,5,7,11,13\}\), and (B) contains odd numbers. Only (2) in (A) is not odd.
Step 2
Why this answer is correct
The correct answer is A. ( {2} ). \(A=\{2,3,5,7,11,13\}\), and (B) contains odd numbers. Only (2) in (A) is not odd.
Step 3
Exam Tip
\(A=\{2,3,5,7,11,13\}\) है और (B) में विषम संख्याएं हैं। (A) में केवल (2) विषम नहीं है।
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यदि \(A=\{2,3,5,7\}\) और \(B=\{5,7,11,13\}\), तो \(A\cup B\) में कितने अवयव हैं?
If \(A=\{2,3,5,7\}\) and \(B=\{5,7,11,13\}\), how many elements are in \(A\cup B\)?
#sets
#union
#counting
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A (4)
B (6)
C (8)
D (2)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={2,3,5,7,11,13}\). Therefore it has (6) elements.
Step 2
Why this answer is correct
The correct answer is B. (6). \(A\cup B={2,3,5,7,11,13}\). Therefore it has (6) elements.
Step 3
Exam Tip
\(A\cup B={2,3,5,7,11,13}\) है। इसलिए इसमें (6) अवयव हैं।
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6\}\), तो कौन-सा कथन सही है?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), which statement is correct?
#sets
#reasoning
#subset
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A (A-B={1,3,5})
B (B-A={2,4,6})
C \(A\cap B={1,3,5}\)
D \(A\cup B=B\)
Explanation opens after your attempt
Correct Answer
A. (A-B={1,3,5})
Step 1
Concept
Since \(B\subseteq A\), (A-B) contains elements of (A) not in (B). They are ({1,3,5}).
Step 2
Why this answer is correct
The correct answer is A. (A-B={1,3,5}). Since \(B\subseteq A\), (A-B) contains elements of (A) not in (B). They are ({1,3,5}).
Step 3
Exam Tip
\(B\subseteq A\) है, इसलिए (A-B) में (A) के वे अवयव हैं जो (B) में नहीं हैं। वे ({1,3,5}) हैं।
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यदि \(A\cup B=A\), तो सही निष्कर्ष क्या है?
If \(A\cup B=A\), what is the correct conclusion?
#sets
#subset
#reasoning
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D \(A-B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
If \(A\cup B=A\), (B) adds no new element outside (A). Therefore \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). If \(A\cup B=A\), (B) adds no new element outside (A). Therefore \(B\subseteq A\).
Step 3
Exam Tip
यदि \(A\cup B=A\), तो (B) का कोई नया अवयव (A) के बाहर नहीं है। इसलिए \(B\subseteq A\)।
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किसी सर्वसमुच्चय (U) के लिए \(A\cup A'\) किसके बराबर है?
For a universal set (U), \(A\cup A'\) is equal to which set?
#sets
#complement
#law
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A (A)
B (A')
C (U)
D \( \varnothing \)
Explanation opens after your attempt
Step 1
Concept
Every element is either in (A) or in (A'). Hence their union is (U).
Step 2
Why this answer is correct
The correct answer is C. (U). Every element is either in (A) or in (A'). Hence their union is (U).
Step 3
Exam Tip
कोई भी अवयव या तो (A) में होगा या (A') में। इसलिए दोनों का संघ (U) होता है।
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किसी सर्वसमुच्चय (U) के लिए \(A\cap A'\) किसके बराबर है?
For a universal set (U), \(A\cap A'\) is equal to which set?
#sets
#complement
#intersection
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A (U)
B (A)
C (A')
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
D. \( \varnothing \)
Step 1
Concept
No element can be in both (A) and (A') at the same time. Therefore the intersection is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is D. \( \varnothing \). No element can be in both (A) and (A') at the same time. Therefore the intersection is \(\varnothing\).
Step 3
Exam Tip
कोई अवयव एक साथ (A) और (A') दोनों में नहीं हो सकता। इसलिए प्रतिच्छेद \(\varnothing\) है।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\) और \(C=\{3,4,7\}\), तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\), and \(C=\{3,4,7\}\), what is (A\cap\(B\cup C\))?
#sets
#distributive
#calculation
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A ( {2,3,4} )
B ( {1,5} )
C ( {3} )
D ( {2,3,4,6,7} )
Explanation opens after your attempt
Correct Answer
A. ( {2,3,4} )
Step 1
Concept
\(B\cup C={2,3,4,6,7}\). Its common part with (A) is ({2,3,4}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,3,4} ). \(B\cup C={2,3,4,6,7}\). Its common part with (A) is ({2,3,4}).
Step 3
Exam Tip
\(B\cup C={2,3,4,6,7}\) है। इसका (A) से सामान्य भाग ({2,3,4}) है।
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यदि \(A=\{1,2,4,8\}\), \(B=\{2,4,6\}\) और \(C=\{4,6,8\}\), तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{1,2,4,8\}\), \(B=\{2,4,6\}\), and \(C=\{4,6,8\}\), what is (\(A\cap B\)\cup C)?
#sets
#mixed-operations
#union
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A ( {2,4,6,8} )
B ( {4} )
C ( {1,2,4,6,8} )
D ( {2,6} )
Explanation opens after your attempt
Correct Answer
A. ( {2,4,6,8} )
Step 1
Concept
\(A\cap B={2,4}\). Combining it with \(C=\{4,6,8\}\) gives ({2,4,6,8}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,4,6,8} ). \(A\cap B={2,4}\). Combining it with \(C=\{4,6,8\}\) gives ({2,4,6,8}).
Step 3
Exam Tip
\(A\cap B={2,4}\) है। इसे \(C=\{4,6,8\}\) से मिलाने पर ({2,4,6,8}) मिलता है।
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\(यदि (A={x:x\) का गुणज 3 है\(, 1\le x\le 20}) और (B={x:x\) का गुणज 5 है\(, 1\le x\le 20}), तो (A\cap B) क्या है\)?
\(If (A={x:x\) is a multiple of \(3, 1\le x\le 20}) and (B={x:x\) is a multiple of \(5, 1\le x\le 20}), what is (A\cap B)\)?
#sets
#multiples
#intersection
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A ( {15} )
B ( {3,5,15} )
C ( {6,10,15} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {15} )
Step 1
Concept
Only (15) up to (20) is a multiple of both (3) and (5). Hence the intersection is ({15}).
Step 2
Why this answer is correct
The correct answer is A. ( {15} ). Only (15) up to (20) is a multiple of both (3) and (5). Hence the intersection is ({15}).
Step 3
Exam Tip
(3) और (5) दोनों के गुणज में (15) ही (20) तक आता है। इसलिए प्रतिच्छेद ({15}) है।
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\(यदि (A={x:x\) का गुणज 4 है\(, 1\le x\le 25}) और (B={x:x\) का गुणज 6 है\(, 1\le x\le 25}), तो (A\cup B) में कितने अवयव हैं\)?
\(If (A={x:x\) is a multiple of \(4, 1\le x\le 25}) and (B={x:x\) is a multiple of \(6, 1\le x\le 25}), how many elements are in (A\cup B)\)?
#sets
#multiples
#cardinality
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(A=\{4,8,12,16,20,24\}\) and \(B=\{6,12,18,24\}\). The union has (9) distinct elements.
Step 2
Why this answer is correct
The correct answer is B. (9). \(A=\{4,8,12,16,20,24\}\) and \(B=\{6,12,18,24\}\). The union has (9) distinct elements.
Step 3
Exam Tip
\(A=\{4,8,12,16,20,24\}\) और \(B=\{6,12,18,24\}\) है। संघ में (9) अलग अवयव हैं।
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यदि \(A=\{1,2,3,4,5,6,7\}\) और \(B=\{2,4,6,8\}\), तो (A-B) और (B-A) का संघ क्या है?
If \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{2,4,6,8\}\), what is the union of (A-B) and (B-A)?
#sets
#symmetric-difference
#difference
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A ( {1,3,5,7,8} )
B ( {2,4,6} )
C ( {1,2,3,4,5,6,7,8} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5,7,8} )
Step 1
Concept
(A-B={1,3,5,7}) and (B-A={8}). Their union is ({1,3,5,7,8}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3,5,7,8} ). (A-B={1,3,5,7}) and (B-A={8}). Their union is ({1,3,5,7,8}).
Step 3
Exam Tip
(A-B={1,3,5,7}) और (B-A={8}) है। उनका संघ ({1,3,5,7,8}) है।
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\(यदि (A={x:x\in \mathbb{N}, x\le 12}) और (B={x:x\in \mathbb{N}, x\) वर्ग संख्या है\(, x\le 12}), तो (A-B) में कितने अवयव हैं\)?
\(If (A={x:x\in \mathbb{N}, x\le 12}) and (B={x:x\in \mathbb{N}, x\) is a square number\(, x\le 12}), how many elements are in (A-B)\)?
#sets
#natural-numbers
#difference
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A (3)
B (9)
C (12)
D (10)
Explanation opens after your attempt
Step 1
Concept
(A) has (12) elements and \(B=\{1,4,9\}\). Thus (A-B) has (12-3=9) elements.
Step 2
Why this answer is correct
The correct answer is B. (9). (A) has (12) elements and \(B=\{1,4,9\}\). Thus (A-B) has (12-3=9) elements.
Step 3
Exam Tip
(A) में (12) अवयव हैं और \(B=\{1,4,9\}\) है। इसलिए (A-B) में (12-3=9) अवयव होंगे।
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कौन-सा विकल्प हमेशा सत्य है?
Which option is always true?
#sets
#true-statement
#reasoning
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A \(A\cup B=A\cap B\)
B (A-B=B-A)
C \(A\cap B\subseteq A\)
D \(A\subseteq A-B\)
Explanation opens after your attempt
Correct Answer
C. \(A\cap B\subseteq A\)
Step 1
Concept
\(A\cap B\) contains only common elements of (A) and (B), so it is a subset of (A). Test always-true statements with examples too.
Step 2
Why this answer is correct
The correct answer is C. \(A\cap B\subseteq A\). \(A\cap B\) contains only common elements of (A) and (B), so it is a subset of (A). Test always-true statements with examples too.
Step 3
Exam Tip
\(A\cap B\) में केवल (A) और (B) के सामान्य अवयव होते हैं, इसलिए यह (A) का उपसमुच्चय है। हमेशा सत्य कथनों को उदाहरण से भी जांचें।
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कौन-सा विकल्प सामान्यतः सत्य नहीं है?
Which option is generally not true?
#sets
#common-mistake
#difference
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A \(A\cup B=B\cup A\)
B \(A\cap B=B\cap A\)
C (A-B=B-A)
D \(A\cup \varnothing=A\)
Explanation opens after your attempt
Correct Answer
C. (A-B=B-A)
Step 1
Concept
Order matters in set difference, so (A-B) and (B-A) are generally not equal. Union and intersection are commutative.
Step 2
Why this answer is correct
The correct answer is C. (A-B=B-A). Order matters in set difference, so (A-B) and (B-A) are generally not equal. Union and intersection are commutative.
Step 3
Exam Tip
समुच्चय अंतर में क्रम महत्वपूर्ण है, इसलिए (A-B) और (B-A) सामान्यतः समान नहीं होते। संघ और प्रतिच्छेद क्रमविनिमेय होते हैं।
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यदि \(A=\{1,2,3\}\), तो \(A\cup \varnothing\) क्या है?
If \(A=\{1,2,3\}\), what is \(A\cup \varnothing\)?
#sets
#empty-set
#union
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A \( \varnothing \)
B ( {1,2,3} )
C ( {0,1,2,3} )
D ( {1} )
Explanation opens after your attempt
Correct Answer
B. ( {1,2,3} )
Step 1
Concept
The empty set has no element, so it adds nothing to the union. Hence \(A\cup \varnothing=A\).
Step 2
Why this answer is correct
The correct answer is B. ( {1,2,3} ). The empty set has no element, so it adds nothing to the union. Hence \(A\cup \varnothing=A\).
Step 3
Exam Tip
रिक्त समुच्चय में कोई अवयव नहीं होता, इसलिए संघ में कुछ नया नहीं जुड़ता। अतः \(A\cup \varnothing=A\)।
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यदि \(A=\{1,2,3\}\), तो \(A\cap \varnothing\) क्या है?
If \(A=\{1,2,3\}\), what is \(A\cap \varnothing\)?
#sets
#empty-set
#intersection
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A (A)
B ( {1,2,3} )
C \( \varnothing \)
D ( {0} )
Explanation opens after your attempt
Correct Answer
C. \( \varnothing \)
Step 1
Concept
The empty set has no element, so there is no common element. Thus the intersection is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \( \varnothing \). The empty set has no element, so there is no common element. Thus the intersection is \(\varnothing\).
Step 3
Exam Tip
रिक्त समुच्चय में कोई अवयव नहीं है, इसलिए कोई सामान्य अवयव नहीं मिलेगा। अतः प्रतिच्छेद \(\varnothing\) है।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (n(A-B)+n(B-A)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (n(A-B)+n(B-A))?
#sets
#cardinality
#difference
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A-B={1,2}) and (B-A={5,6}). Hence (n(A-B)+n(B-A)=2+2=4).
Step 2
Why this answer is correct
The correct answer is B. (4). (A-B={1,2}) and (B-A={5,6}). Hence (n(A-B)+n(B-A)=2+2=4).
Step 3
Exam Tip
(A-B={1,2}) और (B-A={5,6}) है। इसलिए (n(A-B)+n(B-A)=2+2=4)।
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यदि (n\(A\cup B\)=60), (n(A-B)=18) और (n(B-A)=22), तो (n\(A\cap B\)) क्या है?
If (n\(A\cup B\)=60), (n(A-B)=18), and (n(B-A)=22), what is (n\(A\cap B\))?
#sets
#venn-diagram
#cardinality
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A (20)
B (40)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B\) is made of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (n\(A\cap B\)=60-18-22=20).
Step 2
Why this answer is correct
The correct answer is A. (20). \(A\cup B\) is made of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (n\(A\cap B\)=60-18-22=20).
Step 3
Exam Tip
\(A\cup B\) तीन अलग भागों (A-B), (B-A) और \(A\cap B\) से बनता है। इसलिए (n\(A\cap B\)=60-18-22=20)।
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