यदि \(A=\{1,2,3\}\) और \(B=\{3,4,5\}\) हैं, तो \(A\cup B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{3,4,5\}\), then what is \(A\cup B\)?
#sets
#union
#basic
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A ( {1,2,3,4,5} )
B ( {3} )
C ( {1,2} )
D ( {4,5} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,5} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,5} ). \(A\cup B\) contains all distinct elements of both sets. In exams, write repeated elements only once.
Step 3
Exam Tip
\(A\cup B\) में दोनों समुच्चयों के सभी अलग-अलग अवयव आते हैं। परीक्षा में दोहराए गए अवयव को केवल एक बार लिखें।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{1,2,3,4\}\) हैं, तो \(A\cap B\) ज्ञात कीजिए।
If \(A=\{2,4,6,8\}\) and \(B=\{1,2,3,4\}\), find \(A\cap B\).
#sets
#intersection
#basic
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A ( {2,4} )
B ( {1,3,6,8} )
C ( {2,4,6,8} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {2,4} )
Step 1
Concept
\(A\cap B\) contains only elements common to both sets. First identify common elements for quick solving.
Step 2
Why this answer is correct
The correct answer is A. ( {2,4} ). \(A\cap B\) contains only elements common to both sets. First identify common elements for quick solving.
Step 3
Exam Tip
\(A\cap B\) में केवल वे अवयव आते हैं जो दोनों में समान हों। पहले समान अवयवों को पहचानना आसान तरीका है।
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यदि \(A=\{a,b,c,d\}\) और \(B=\{b,d,e\}\) हैं, तो (A-B) क्या होगा?
If \(A=\{a,b,c,d\}\) and \(B=\{b,d,e\}\), what will be (A-B)?
#sets
#difference
#basic
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A ( {a,c} )
B ( {b,d} )
C ( {a,b,c,d,e} )
D ( {e} )
Explanation opens after your attempt
Correct Answer
A. ( {a,c} )
Step 1
Concept
(A-B) contains elements of (A) that are not in (B). In set difference, changing order can change the answer.
Step 2
Why this answer is correct
The correct answer is A. ( {a,c} ). (A-B) contains elements of (A) that are not in (B). In set difference, changing order can change the answer.
Step 3
Exam Tip
(A-B) में (A) के वे अवयव आते हैं जो (B) में नहीं हैं। घटाने में क्रम बदलने से उत्तर बदल सकता है।
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यदि \(P={x:x\in \mathbb{N},x<5}\) और \(Q=\{2,4,6\}\) हैं, तो \(P\cup Q\) कौन-सा है?
If \(P={x:x\in \mathbb{N},x<5}\) and \(Q=\{2,4,6\}\), which is \(P\cup Q\)?
#sets
#union
#set-builder
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A ( {1,2,3,4,6} )
B ( {2,4} )
C ( {1,3,6} )
D ( {1,2,3,4} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4,6} )
Step 1
Concept
\(P=\{1,2,3,4\}\), so \(P\cup Q={1,2,3,4,6}\). Convert set-builder form to roster form first.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4,6} ). \(P=\{1,2,3,4\}\), so \(P\cup Q={1,2,3,4,6}\). Convert set-builder form to roster form first.
Step 3
Exam Tip
\(P=\{1,2,3,4\}\) है, इसलिए \(P\cup Q={1,2,3,4,6}\) है। पहले set-builder form को roster form में बदलें।
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यदि \(A=\{5,10,15\}\) और \(B=\{20,25\}\) हैं, तो \(A\cap B\) क्या है?
If \(A=\{5,10,15\}\) and \(B=\{20,25\}\), what is \(A\cap B\)?
#sets
#intersection
#disjoint
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A \( \varnothing \)
B ( {5,10,15,20,25} )
C ( {5,20} )
D ( {10,25} )
Explanation opens after your attempt
Correct Answer
A. \( \varnothing \)
Step 1
Concept
There is no common element, so \(A\cap B=\varnothing\). Such sets are disjoint sets.
Step 2
Why this answer is correct
The correct answer is A. \( \varnothing \). There is no common element, so \(A\cap B=\varnothing\). Such sets are disjoint sets.
Step 3
Exam Tip
दोनों समुच्चयों में कोई समान अवयव नहीं है, इसलिए \(A\cap B=\varnothing\) है। ऐसे समुच्चय असंयुक्त होते हैं।
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यदि \(X=\{1,3,5,7\}\) और \(Y=\{3,7,9\}\) हैं, तो (Y-X) ज्ञात कीजिए।
If \(X=\{1,3,5,7\}\) and \(Y=\{3,7,9\}\), find (Y-X).
#sets
#difference
#order
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A ( {9} )
B ( {1,5} )
C ( {3,7} )
D ( {1,3,5,7,9} )
Explanation opens after your attempt
Correct Answer
A. ( {9} )
Step 1
Concept
(Y-X) contains elements of (Y) that are not in (X). Here only (9) satisfies this.
Step 2
Why this answer is correct
The correct answer is A. ( {9} ). (Y-X) contains elements of (Y) that are not in (X). Here only (9) satisfies this.
Step 3
Exam Tip
(Y-X) में (Y) के वे अवयव हैं जो (X) में नहीं हैं। यहां (9) ही ऐसा अवयव है।
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यदि \(A=\{1,2\}\), \(B=\{2,3\}\) और \(C=\{3,4\}\) हैं, तो \(A\cup B\cup C\) क्या है?
If \(A=\{1,2\}\), \(B=\{2,3\}\), and \(C=\{3,4\}\), what is \(A\cup B\cup C\)?
#sets
#union
#three-sets
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A ( {1,2,3,4} )
B ( {2,3} )
C ( {1,4} )
D ( {1,2,2,3,3,4} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4} )
Step 1
Concept
Union takes all distinct elements. Repetition is not needed in a set.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4} ). Union takes all distinct elements. Repetition is not needed in a set.
Step 3
Exam Tip
संघ में सभी अलग-अलग अवयव लिए जाते हैं। दोहराव लिखना समुच्चय में आवश्यक नहीं होता।
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यदि \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\) और \(C=\{3,5,11\}\) हैं, तो \(A\cap B\cap C\) क्या है?
If \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\), and \(C=\{3,5,11\}\), what is \(A\cap B\cap C\)?
#sets
#intersection
#three-sets
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A ( {3,5} )
B ( {2,7} )
C ( {1,9,11} )
D ( {2,3,5,7,9,11} )
Explanation opens after your attempt
Correct Answer
A. ( {3,5} )
Step 1
Concept
The elements common to all three sets are (3) and (5). \(A\cap B\cap C\) contains only elements common to every set.
Step 2
Why this answer is correct
The correct answer is A. ( {3,5} ). The elements common to all three sets are (3) and (5). \(A\cap B\cap C\) contains only elements common to every set.
Step 3
Exam Tip
तीनों समुच्चयों में समान अवयव (3) और (5) हैं। \(A\cap B\cap C\) में केवल सभी में सामान्य अवयव आते हैं।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{2,4\}\) हैं, तो (B-A) क्या है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{2,4\}\), what is (B-A)?
#sets
#difference
#subset
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A \( \varnothing \)
B ( {1,3,5} )
C ( {2,4} )
D ( {1,2,3,4,5} )
Explanation opens after your attempt
Correct Answer
A. \( \varnothing \)
Step 1
Concept
Every element of (B) is in (A), so \(B-A=\varnothing\). If \(B\subset A\), then (B-A) may be empty.
Step 2
Why this answer is correct
The correct answer is A. \( \varnothing \). Every element of (B) is in (A), so \(B-A=\varnothing\). If \(B\subset A\), then (B-A) may be empty.
Step 3
Exam Tip
(B) का हर अवयव (A) में है, इसलिए \(B-A=\varnothing\) है। यदि \(B\subset A\), तो (B-A) खाली हो सकता है।
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यदि \(A\subseteq B\) है, तो \(A\cup B\) किसके बराबर होगा?
If \(A\subseteq B\), then \(A\cup B\) will be equal to what?
#sets
#union
#subset-property
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A (B)
B (A)
C (A-B)
D \(A\cap B\)
Explanation opens after your attempt
Step 1
Concept
If \(A\subseteq B\), then (B) already contains all elements of (A). Therefore, \(A\cup B=B\).
Step 2
Why this answer is correct
The correct answer is A. (B). If \(A\subseteq B\), then (B) already contains all elements of (A). Therefore, \(A\cup B=B\).
Step 3
Exam Tip
यदि \(A\subseteq B\), तो (B) में (A) के सभी अवयव पहले से हैं। इसलिए \(A\cup B=B\) होता है।
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यदि \(A\subseteq B\) है, तो \(A\cap B\) किसके बराबर होगा?
If \(A\subseteq B\), then \(A\cap B\) will be equal to what?
#sets
#intersection
#subset-property
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A (A)
B (B)
C \(A\cup B\)
D (B-A)
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\), all elements of (A) are common to both sets. Hence \(A\cap B=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). When \(A\subseteq B\), all elements of (A) are common to both sets. Hence \(A\cap B=A\).
Step 3
Exam Tip
जब \(A\subseteq B\), तब (A) के सभी अवयव दोनों में सामान्य होते हैं। अतः \(A\cap B=A\) है।
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यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4\}\) हैं, तो (\(A\cup B\)) क्या है?
If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is (\(A\cup B\))?
#sets
#union
#universal-set
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A ( {1,2,3,4} )
B ( {3} )
C ( {5,6} )
D ( {1,2,4} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,4} )
Step 1
Concept
\(A\cup B\) contains all distinct elements of (A) and (B). (U) only gives the universal set here.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,4} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) only gives the universal set here.
Step 3
Exam Tip
\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) यहां केवल सार्वत्रिक समुच्चय की जानकारी देता है।
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यदि \(A=\{2,4,6,8,10\}\) और \(B=\{4,8,12\}\) हैं, तो (A-B) कौन-सा है?
If \(A=\{2,4,6,8,10\}\) and \(B=\{4,8,12\}\), which is (A-B)?
#sets
#difference
#common-elements
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A ( {2,6,10} )
B ( {4,8} )
C ( {12} )
D ( {2,4,6,8,10,12} )
Explanation opens after your attempt
Correct Answer
A. ( {2,6,10} )
Step 1
Concept
In (A-B), common elements of (B) are removed from (A). Removing (4) and (8) gives ({2,6,10}).
Step 2
Why this answer is correct
The correct answer is A. ( {2,6,10} ). In (A-B), common elements of (B) are removed from (A). Removing (4) and (8) gives ({2,6,10}).
Step 3
Exam Tip
(A-B) में (A) से (B) के सामान्य अवयव हटाए जाते हैं। इसलिए (4) और (8) हटाकर ({2,6,10}) मिलता है।
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यदि \(A=\{1,2,3\}\) है, तो \(A\cup \varnothing\) क्या होगा?
If \(A=\{1,2,3\}\), what will \(A\cup \varnothing\) be?
#sets
#union
#empty-set
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A ( {1,2,3} )
B \( \varnothing \)
C ( {0,1,2,3} )
D ( {1,2} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
The empty set has no elements, so \(A\cup \varnothing=A\). This is the identity property of union.
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). The empty set has no elements, so \(A\cup \varnothing=A\). This is the identity property of union.
Step 3
Exam Tip
खाली समुच्चय में कोई अवयव नहीं होता, इसलिए \(A\cup \varnothing=A\) है। यह संघ का पहचान गुण है।
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यदि \(A=\{4,5,6\}\) है, तो \(A\cap \varnothing\) क्या होगा?
If \(A=\{4,5,6\}\), what will \(A\cap \varnothing\) be?
#sets
#intersection
#empty-set
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A \( \varnothing \)
B ( {4,5,6} )
C ( {0} )
D ( {4} )
Explanation opens after your attempt
Correct Answer
A. \( \varnothing \)
Step 1
Concept
\(\varnothing\) has no element, so no common element can exist. Thus \(A\cap \varnothing=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \( \varnothing \). \(\varnothing\) has no element, so no common element can exist. Thus \(A\cap \varnothing=\varnothing\).
Step 3
Exam Tip
\(\varnothing\) में कोई अवयव नहीं है, इसलिए कोई सामान्य अवयव नहीं मिलेगा। अतः \(A\cap \varnothing=\varnothing\) है।
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यदि \(A=\{p,q,r\}\) है, तो (A-A) क्या होगा?
If \(A=\{p,q,r\}\), what will (A-A) be?
#sets
#difference
#same-set
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A \( \varnothing \)
B ( {p,q,r} )
C ( {p} )
D ( {q,r} )
Explanation opens after your attempt
Correct Answer
A. \( \varnothing \)
Step 1
Concept
(A-A) needs elements of (A) that are not in (A), which is impossible. So \(A-A=\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \( \varnothing \). (A-A) needs elements of (A) that are not in (A), which is impossible. So \(A-A=\varnothing\).
Step 3
Exam Tip
(A-A) में (A) के वे अवयव चाहिए जो (A) में न हों, जो संभव नहीं है। इसलिए \(A-A=\varnothing\) है।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\) हैं, तो (\(A\cup B\)-\(A\cap B\)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is (\(A\cup B\)-\(A\cap B\))?
#sets
#union
#intersection
#difference
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A ( {1,2,5,6} )
B ( {3,4} )
C ( {1,2,3,4,5,6} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {1,2,5,6} )
Step 1
Concept
\(A\cup B={1,2,3,4,5,6}\) and \(A\cap B={3,4}\). Removing the common part gives ({1,2,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,5,6} ). \(A\cup B={1,2,3,4,5,6}\) and \(A\cap B={3,4}\). Removing the common part gives ({1,2,5,6}).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6}\) और \(A\cap B={3,4}\) है। सामान्य भाग हटाने पर ({1,2,5,6}) मिलता है।
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\(यदि (A={x:x\) is a vowel in English\(}) और (B={a,e,i}) हैं, तो (B\subseteq A) के आधार पर (A\cup B) क्या है\)?
\(If (A={x:x\) is a vowel in English\(}) and (B={a,e,i}), then using (B\subseteq A), what is (A\cup B)\)?
#sets
#union
#subset
#letters
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A ( {a,e,i,o,u} )
B ( {a,e,i} )
C ( {o,u} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {a,e,i,o,u} )
Step 1
Concept
\(A=\{a,e,i,o,u\}\) and \(B\subseteq A\), so \(A\cup B=A\). The larger set already includes the smaller set's elements.
Step 2
Why this answer is correct
The correct answer is A. ( {a,e,i,o,u} ). \(A=\{a,e,i,o,u\}\) and \(B\subseteq A\), so \(A\cup B=A\). The larger set already includes the smaller set's elements.
Step 3
Exam Tip
\(A=\{a,e,i,o,u\}\) और \(B\subseteq A\) है, इसलिए \(A\cup B=A\) है। बड़े समुच्चय में छोटे के अवयव पहले से शामिल होते हैं।
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\(यदि (A={x:x\in \mathbb{N},x\leq 6}) और (B={x:x\in \mathbb{N},x\) is even\(,x\leq 8}) हैं, तो (A\cap B) क्या है\)?
\(If (A={x:x\in \mathbb{N},x\leq 6}) and (B={x:x\in \mathbb{N},x\) is even\(,x\leq 8}), what is (A\cap B)\)?
#sets
#intersection
#set-builder
#natural-numbers
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A ( {2,4,6} )
B ( {1,3,5} )
C ( {2,4,6,8} )
D ( {1,2,3,4,5,6,8} )
Explanation opens after your attempt
Correct Answer
A. ( {2,4,6} )
Step 1
Concept
\(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6,8\}\). The common elements are (2,4,6).
Step 2
Why this answer is correct
The correct answer is A. ( {2,4,6} ). \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6,8\}\). The common elements are (2,4,6).
Step 3
Exam Tip
\(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6,8\}\) है। सामान्य अवयव (2,4,6) हैं।
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यदि \(A=\{0,1,2,3\}\) और \(B=\{2,3,4,5\}\) हैं, तो (A-B) और (B-A) के बारे में सही कथन कौन-सा है?
If \(A=\{0,1,2,3\}\) and \(B=\{2,3,4,5\}\), which statement about (A-B) and (B-A) is correct?
#sets
#difference
#non-commutative
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A (A-B={0,1}) और (B-A={4,5}) / (A-B={0,1}) and (B-A={4,5})
B (A-B=B-A)
C (A-B={2,3}) और (B-A={2,3}) / (A-B={2,3}) and (B-A={2,3})
D \(A-B=\varnothing\) और \(B-A=\varnothing\) / \(A-B=\varnothing\) and \(B-A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (A-B={0,1}) और (B-A={4,5}) / (A-B={0,1}) and (B-A={4,5})
Step 1
Concept
(0,1) remain in (A-B), and (4,5) remain in (B-A). Set difference is generally not commutative.
Step 2
Why this answer is correct
The correct answer is A. (A-B={0,1}) और (B-A={4,5}) / (A-B={0,1}) and (B-A={4,5}). (0,1) remain in (A-B), and (4,5) remain in (B-A). Set difference is generally not commutative.
Step 3
Exam Tip
(A-B) में (0,1) और (B-A) में (4,5) बचते हैं। समुच्चय अंतर सामान्यतः क्रमविनिमेय नहीं होता।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,2,1\}\) हैं, तो \(A\cup B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{3,2,1\}\), what is \(A\cup B\)?
#sets
#union
#equal-sets
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A ( {1,2,3} )
B ( {1,2,3,3,2,1} )
C \( \varnothing \)
D ( {6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
Order and repetition do not matter in sets. Therefore (A=B) and \(A\cup B=A\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). Order and repetition do not matter in sets. Therefore (A=B) and \(A\cup B=A\).
Step 3
Exam Tip
समुच्चय में क्रम और दोहराव का महत्व नहीं होता। इसलिए (A=B) और \(A\cup B=A\) है।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,2,1\}\) हैं, तो \(A\cap B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{3,2,1\}\), what is \(A\cap B\)?
#sets
#intersection
#equal-sets
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A ( {1,2,3} )
B \( \varnothing \)
C ( {3} )
D ( {1} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
Both sets are equal, so all elements are common. Hence \(A\cap B={1,2,3}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). Both sets are equal, so all elements are common. Hence \(A\cap B={1,2,3}\).
Step 3
Exam Tip
दोनों समुच्चय समान हैं, इसलिए सभी अवयव सामान्य हैं। अतः \(A\cap B={1,2,3}\) है।
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यदि \(A=\{1,4,9,16\}\) और \(B=\{1,2,4,8,16\}\) हैं, तो \(A\cap B\) कौन-सा है?
If \(A=\{1,4,9,16\}\) and \(B=\{1,2,4,8,16\}\), which is \(A\cap B\)?
#sets
#intersection
#numerical
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A ( {1,4,16} )
B ( {9} )
C ( {2,8} )
D ( {1,2,4,8,9,16} )
Explanation opens after your attempt
Correct Answer
A. ( {1,4,16} )
Step 1
Concept
The elements present in both sets are (1,4,16). (9) is only in (A), so it will not be in the intersection.
Step 2
Why this answer is correct
The correct answer is A. ( {1,4,16} ). The elements present in both sets are (1,4,16). (9) is only in (A), so it will not be in the intersection.
Step 3
Exam Tip
दोनों में मौजूद अवयव (1,4,16) हैं। (9) केवल (A) में है, इसलिए वह intersection में नहीं आएगा।
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यदि \(A=\{red,blue,green\}\) और \(B=\{blue,yellow\}\) हैं, तो \(A\cup B\) क्या है?
If \(A=\{red,blue,green\}\) and \(B=\{blue,yellow\}\), what is \(A\cup B\)?
#sets
#union
#word-set
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A ( {red,blue,green,yellow} )
B ( {blue} )
C ( {red,green} )
D ( {yellow} )
Explanation opens after your attempt
Correct Answer
A. ( {red,blue,green,yellow} )
Step 1
Concept
Union takes all colors from both sets once. (blue) is repeated, so it is written only once.
Step 2
Why this answer is correct
The correct answer is A. ( {red,blue,green,yellow} ). Union takes all colors from both sets once. (blue) is repeated, so it is written only once.
Step 3
Exam Tip
संघ में दोनों समुच्चयों के सभी रंग एक बार लिए जाते हैं। (blue) दोहराया हुआ है, इसलिए एक बार लिखा जाएगा।
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यदि \(A=\{red,blue,green\}\) और \(B=\{blue,yellow\}\) हैं, तो (A-B) क्या है?
If \(A=\{red,blue,green\}\) and \(B=\{blue,yellow\}\), what is (A-B)?
#sets
#difference
#word-set
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A ( {red,green} )
B ( {blue} )
C ( {yellow} )
D ( {red,blue,green,yellow} )
Explanation opens after your attempt
Correct Answer
A. ( {red,green} )
Step 1
Concept
The common element (blue) is removed from (A). Therefore (A-B={red,green}).
Step 2
Why this answer is correct
The correct answer is A. ( {red,green} ). The common element (blue) is removed from (A). Therefore (A-B={red,green}).
Step 3
Exam Tip
(A) से (B) का सामान्य अवयव (blue) हटेगा। इसलिए (A-B={red,green}) है।
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यदि (n(A)=5), (n(B)=4) और (n\(A\cap B\)=2) हैं, तो (n\(A\cup B\)) क्या होगा?
If (n(A)=5), (n(B)=4), and (n\(A\cap B\)=2), what will (n\(A\cup B\)) be?
#sets
#cardinality
#union-formula
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A (7)
B (9)
C (2)
D (11)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (5+4-2=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Thus (5+4-2=7).
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाएं। इसलिए (5+4-2=7) है।
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यदि (n(A)=8), (n(B)=6) और (n\(A\cup B\)=10) हैं, तो (n\(A\cap B\)) क्या है?
If (n(A)=8), (n(B)=6), and (n\(A\cup B\)=10), what is (n\(A\cap B\))?
#sets
#cardinality
#intersection
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A (4)
B (2)
C (14)
D (10)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)). Hence (8+6-10=4).
Step 2
Why this answer is correct
The correct answer is A. (4). (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)). Hence (8+6-10=4).
Step 3
Exam Tip
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)) होता है। अतः (8+6-10=4) है।
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यदि \(A\cap B=\varnothing\), (n(A)=3) और (n(B)=5) हैं, तो (n\(A\cup B\)) क्या है?
If \(A\cap B=\varnothing\), (n(A)=3), and (n(B)=5), what is (n\(A\cup B\))?
#sets
#cardinality
#disjoint-union
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A (8)
B (2)
C (15)
D (0)
Explanation opens after your attempt
Step 1
Concept
For disjoint sets, (n\(A\cap B\)=0). Therefore (n\(A\cup B\)=3+5=8).
Step 2
Why this answer is correct
The correct answer is A. (8). For disjoint sets, (n\(A\cap B\)=0). Therefore (n\(A\cup B\)=3+5=8).
Step 3
Exam Tip
असंयुक्त समुच्चयों में (n\(A\cap B\)=0) होता है। इसलिए (n\(A\cup B\)=3+5=8) है।
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{2,4,6\}\) हैं, तो (A-B) में कितने अवयव हैं?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{2,4,6\}\), how many elements are in (A-B)?
#sets
#difference
#cardinality
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A (3)
B (6)
C (0)
D (9)
Explanation opens after your attempt
Step 1
Concept
(A-B={1,3,5}), so it has (3) elements. First find the difference, then count.
Step 2
Why this answer is correct
The correct answer is A. (3). (A-B={1,3,5}), so it has (3) elements. First find the difference, then count.
Step 3
Exam Tip
(A-B={1,3,5}) है, इसलिए इसमें (3) अवयव हैं। पहले अंतर निकालें, फिर गिनें।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{4,5,6\}\) हैं, तो (n\(A\cup B\)) क्या है?
If \(A=\{1,2,3,4\}\) and \(B=\{4,5,6\}\), what is (n\(A\cup B\))?
#sets
#union
#cardinality
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A (6)
B (7)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4,5,6}\). Therefore (n\(A\cup B\)=6).
Step 2
Why this answer is correct
The correct answer is A. (6). \(A\cup B={1,2,3,4,5,6}\). Therefore (n\(A\cup B\)=6).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,5,6}\) है। इसलिए (n\(A\cup B\)=6) है।
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यदि \(A=\{2,3,4,5\}\) और \(B=\{1,3,5,7\}\) हैं, तो (n\(A\cap B\)) क्या है?
If \(A=\{2,3,4,5\}\) and \(B=\{1,3,5,7\}\), what is (n\(A\cap B\))?
#sets
#intersection
#cardinality
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A (2)
B (4)
C (6)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B={3,5}\). So it has (2) elements.
Step 2
Why this answer is correct
The correct answer is A. (2). \(A\cap B={3,5}\). So it has (2) elements.
Step 3
Exam Tip
\(A\cap B={3,5}\) है। इसलिए इसमें (2) अवयव हैं।
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कौन-सा गुण \(A\cup B=B\cup A\) को दर्शाता है?
Which property is shown by \(A\cup B=B\cup A\)?
#sets
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#property
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A क्रमविनिमेय गुण / Commutative property
B साहचर्य गुण / Associative property
C वितरण गुण / Distributive property
D पहचान गुण / Identity property
Explanation opens after your attempt
Correct Answer
A. क्रमविनिमेय गुण / Commutative property
Step 1
Concept
In \(A\cup B=B\cup A\), changing the order does not change the union. This is the commutative property of union.
Step 2
Why this answer is correct
The correct answer is A. क्रमविनिमेय गुण / Commutative property. In \(A\cup B=B\cup A\), changing the order does not change the union. This is the commutative property of union.
Step 3
Exam Tip
\(A\cup B=B\cup A\) में क्रम बदलने पर संघ नहीं बदलता। यह संघ का क्रमविनिमेय गुण है।
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कौन-सा गुण \(A\cap B=B\cap A\) को दर्शाता है?
Which property is shown by \(A\cap B=B\cap A\)?
#sets
#intersection
#property
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A क्रमविनिमेय गुण / Commutative property
B समुच्चय अंतर गुण / Set difference property
C रिक्त समुच्चय गुण / Empty set property
D पूरक गुण / Complement property
Explanation opens after your attempt
Correct Answer
A. क्रमविनिमेय गुण / Commutative property
Step 1
Concept
In \(A\cap B=B\cap A\), changing the order of intersection does not change the result. This is called the commutative property.
Step 2
Why this answer is correct
The correct answer is A. क्रमविनिमेय गुण / Commutative property. In \(A\cap B=B\cap A\), changing the order of intersection does not change the result. This is called the commutative property.
Step 3
Exam Tip
\(A\cap B=B\cap A\) में intersection का क्रम बदलने से परिणाम नहीं बदलता। इसे क्रमविनिमेय गुण कहते हैं।
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कौन-सा विकल्प \(A\cup A\) के बराबर है?
Which option is equal to \(A\cup A\)?
#sets
#union
#idempotent
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A (A)
B \(\varnothing\)
C (A-A)
D \(A\cap \varnothing\)
Explanation opens after your attempt
Step 1
Concept
The union of a set with itself is the same set. Hence \(A\cup A=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). The union of a set with itself is the same set. Hence \(A\cup A=A\).
Step 3
Exam Tip
किसी समुच्चय का अपने साथ संघ वही समुच्चय होता है। इसलिए \(A\cup A=A\) है।
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कौन-सा विकल्प \(A\cap A\) के बराबर है?
Which option is equal to \(A\cap A\)?
#sets
#intersection
#idempotent
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A (A)
B \(\varnothing\)
C \(A\cup \varnothing\)
D (A-A)
Explanation opens after your attempt
Step 1
Concept
The intersection of a set with itself is the same set. Hence \(A\cap A=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). The intersection of a set with itself is the same set. Hence \(A\cap A=A\).
Step 3
Exam Tip
किसी समुच्चय का अपने साथ सर्वनिष्ठ वही समुच्चय होता है। इसलिए \(A\cap A=A\) है।
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यदि \(A=\{1,2,3\}\), \(B=\{3,4\}\) और \(C=\{4,5\}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5\}\), what is (\(A\cup B\)\cap C)?
#sets
#union
#intersection
#operation-order
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A ( {4} )
B ( {3} )
C ( {1,2,3,4,5} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {4} )
Step 1
Concept
First find \(A\cup B={1,2,3,4}\). Then the common element with (C) is (4).
Step 2
Why this answer is correct
The correct answer is A. ( {4} ). First find \(A\cup B={1,2,3,4}\). Then the common element with (C) is (4).
Step 3
Exam Tip
पहले \(A\cup B={1,2,3,4}\) निकालें। फिर (C) से सामान्य अवयव (4) है।
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यदि \(A=\{1,2,3,4\}\), \(B=\{2,4,6\}\) और \(C=\{1,2,6\}\) हैं, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{1,2,3,4\}\), \(B=\{2,4,6\}\), and \(C=\{1,2,6\}\), what is (\(A\cap B\)\cup C)?
#sets
#intersection
#union
#mixed
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A ( {1,2,4,6} )
B ( {2,4} )
C ( {1,6} )
D ( {3} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,4,6} )
Step 1
Concept
\(A\cap B={2,4}\). Taking union with (C) gives ({1,2,4,6}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,4,6} ). \(A\cap B={2,4}\). Taking union with (C) gives ({1,2,4,6}).
Step 3
Exam Tip
\(A\cap B={2,4}\) है। इसे (C) से मिलाने पर ({1,2,4,6}) मिलता है।
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यदि \(A=\{2,4,6,8\}\), \(B=\{4,8\}\) और \(C=\{8,10\}\) हैं, तो \((A-B)\cup C\) क्या है?
If \(A=\{2,4,6,8\}\), \(B=\{4,8\}\), and \(C=\{8,10\}\), what is \((A-B)\cup C\)?
#sets
#difference
#union
#mixed
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A ( {2,6,8,10} )
B ( {4,8} )
C ( {2,4,6,8,10} )
D ( {10} )
Explanation opens after your attempt
Correct Answer
A. ( {2,6,8,10} )
Step 1
Concept
(A-B={2,6}). Then \({2,6}\cup C={2,6,8,10}\).
Step 2
Why this answer is correct
The correct answer is A. ( {2,6,8,10} ). (A-B={2,6}). Then \({2,6}\cup C={2,6,8,10}\).
Step 3
Exam Tip
(A-B={2,6}) है। फिर \({2,6}\cup C={2,6,8,10}\) मिलता है।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,5\}\) और \(C=\{5,6\}\) हैं, तो \((A-B)\cap C\) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,5\}\), and \(C=\{5,6\}\), what is \((A-B)\cap C\)?
#sets
#difference
#intersection
#mixed
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A \( \varnothing \)
B ( {5} )
C ( {1,3,4} )
D ( {6} )
Explanation opens after your attempt
Correct Answer
A. \( \varnothing \)
Step 1
Concept
(A-B={1,3,4}). It has no common element with \(C=\{5,6\}\).
Step 2
Why this answer is correct
The correct answer is A. \( \varnothing \). (A-B={1,3,4}). It has no common element with \(C=\{5,6\}\).
Step 3
Exam Tip
(A-B={1,3,4}) है। इसका \(C=\{5,6\}\) से कोई सामान्य अवयव नहीं है।
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यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4\}\) हैं, तो कौन-सा अवयव \(A\cup B\) में है पर \(A\cap B\) में नहीं है?
If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), which element is in \(A\cup B\) but not in \(A\cap B\)?
#sets
#union
#intersection
#reasoning
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A (1)
B (2)
C (3)
D (2) और (3) / (2) and (3)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4}\) and \(A\cap B={2,3}\). Among the options, (1) is in the union but not in the intersection.
Step 2
Why this answer is correct
The correct answer is A. (1). \(A\cup B={1,2,3,4}\) and \(A\cap B={2,3}\). Among the options, (1) is in the union but not in the intersection.
Step 3
Exam Tip
\(A\cup B={1,2,3,4}\) और \(A\cap B={2,3}\) है। दिए गए विकल्पों में (1) union में है लेकिन intersection में नहीं है।
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यदि \(A-B=\varnothing\) है, तो कौन-सा निष्कर्ष सही है?
If \(A-B=\varnothing\), which conclusion is correct?
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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
\(A-B=\varnothing\) means every element of (A) is in (B). Therefore \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). \(A-B=\varnothing\) means every element of (A) is in (B). Therefore \(A\subseteq B\).
Step 3
Exam Tip
\(A-B=\varnothing\) का अर्थ है कि (A) का हर अवयव (B) में है। इसलिए \(A\subseteq B\) है।
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यदि \(A\cap B=A\) है, तो कौन-सा निष्कर्ष सही है?
If \(A\cap B=A\), which conclusion is correct?
#sets
#intersection
#subset-reasoning
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A=B^c\)
D \(A\cup B=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
\(A\cap B=A\) shows that all elements of (A) are also in (B). Hence \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). \(A\cap B=A\) shows that all elements of (A) are also in (B). Hence \(A\subseteq B\).
Step 3
Exam Tip
\(A\cap B=A\) बताता है कि (A) के सभी अवयव (B) में भी हैं। इसलिए \(A\subseteq B\) है।
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यदि \(A\cup B=A\) है, तो कौन-सा निष्कर्ष सही है?
If \(A\cup B=A\), which conclusion is correct?
#sets
#union
#subset-reasoning
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A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A\cap B=\varnothing\)
D (B-A=B)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
\(A\cup B=A\) means all elements of (B) are already in (A). Hence \(B\subseteq A\).
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). \(A\cup B=A\) means all elements of (B) are already in (A). Hence \(B\subseteq A\).
Step 3
Exam Tip
\(A\cup B=A\) का अर्थ है कि (B) के सभी अवयव (A) में पहले से हैं। अतः \(B\subseteq A\) है।
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यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\) और (C=A-B) है, तो (C) क्या है?
If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\), and (C=A-B), what is (C)?
#sets
#difference
#application
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A ( {1,3,5} )
B ( {2,4} )
C ( {6} )
D ( {1,2,3,4,5,6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,3,5} )
Step 1
Concept
Elements (2) and (4) of (B) are removed from (A). Therefore \(C=\{1,3,5\}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,3,5} ). Elements (2) and (4) of (B) are removed from (A). Therefore \(C=\{1,3,5\}\).
Step 3
Exam Tip
(A) से (B) के अवयव (2) और (4) हटते हैं। इसलिए \(C=\{1,3,5\}\) है।
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कक्षा में क्रिकेट खेलने वाले छात्रों का समुच्चय \(C=\{Amit,Ravi,Sita\}\) और फुटबॉल खेलने वाले छात्रों का समुच्चय \(F=\{Ravi,Neha\}\) है। दोनों खेलों में कौन है?
In a class, the set of students playing cricket is \(C=\{Amit,Ravi,Sita\}\) and the set of students playing football is \(F=\{Ravi,Neha\}\). Who plays both games?
#sets
#intersection
#word-problem
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A ( {Ravi} )
B ( {Amit,Sita} )
C ( {Neha} )
D ( {Amit,Ravi,Sita,Neha} )
Explanation opens after your attempt
Correct Answer
A. ( {Ravi} )
Step 1
Concept
The name present in both games belongs to \(C\cap F\). Here \(C\cap F={Ravi}\).
Step 2
Why this answer is correct
The correct answer is A. ( {Ravi} ). The name present in both games belongs to \(C\cap F\). Here \(C\cap F={Ravi}\).
Step 3
Exam Tip
दोनों खेलों में आने वाला नाम \(C\cap F\) में होगा। यहां \(C\cap F={Ravi}\) है।
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एक पुस्तकालय में हिंदी पुस्तकें \(H={h_1,h_2,h_3}\) और अंग्रेजी पुस्तकें \(E={h_3,e_1,e_2}\) हैं। कम से कम एक श्रेणी की पुस्तकों का समुच्चय कौन-सा है?
In a library, Hindi books are \(H={h_1,h_2,h_3}\) and English books are \(E={h_3,e_1,e_2}\). Which set represents books in at least one category?
#sets
#union
#word-problem
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A \(H\cup E={h_1,h_2,h_3,e_1,e_2}\)
B \(H\cap E={h_3}\)
C \(H-E={h_1,h_2}\)
D \(E-H={e_1,e_2}\)
Explanation opens after your attempt
Correct Answer
A. \(H\cup E={h_1,h_2,h_3,e_1,e_2}\)
Step 1
Concept
At least one category means union. Therefore the answer is \(H\cup E\).
Step 2
Why this answer is correct
The correct answer is A. \(H\cup E={h_1,h_2,h_3,e_1,e_2}\). At least one category means union. Therefore the answer is \(H\cup E\).
Step 3
Exam Tip
कम से कम एक श्रेणी का अर्थ संघ होता है। इसलिए उत्तर \(H\cup E\) है।
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\(यदि (A={x:x\) is a factor of \(12}) और (B={x:x\) is a factor of \(18}) हैं, तो (A\cap B) क्या है\)?
\(If (A={x:x\) is a factor of \(12}) and (B={x:x\) is a factor of \(18}), what is (A\cap B)\)?
#sets
#intersection
#factors
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A ( {1,2,3,6} )
B ( {1,2,3,4,6,9,12,18} )
C ( {4,12} )
D ( {9,18} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,6} )
Step 1
Concept
The common factors of (12) and (18) are (1,2,3,6). Hence \(A\cap B={1,2,3,6}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,6} ). The common factors of (12) and (18) are (1,2,3,6). Hence \(A\cap B={1,2,3,6}\).
Step 3
Exam Tip
(12) और (18) के समान गुणनखंड (1,2,3,6) हैं। अतः \(A\cap B={1,2,3,6}\) है।
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\(यदि (A={x:x\) is a factor of \(10}) और (B={x:x\) is a factor of \(15}) हैं, तो (A\cup B) क्या है\)?
\(If (A={x:x\) is a factor of \(10}) and (B={x:x\) is a factor of \(15}), what is (A\cup B)\)?
#sets
#union
#factors
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A ( {1,2,3,5,10,15} )
B ( {1,5} )
C ( {2,10} )
D ( {3,15} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3,5,10,15} )
Step 1
Concept
\(A=\{1,2,5,10\}\) and \(B=\{1,3,5,15\}\). The union contains all distinct elements ({1,2,3,5,10,15}).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3,5,10,15} ). \(A=\{1,2,5,10\}\) and \(B=\{1,3,5,15\}\). The union contains all distinct elements ({1,2,3,5,10,15}).
Step 3
Exam Tip
\(A=\{1,2,5,10\}\) और \(B=\{1,3,5,15\}\) है। संघ में सभी अलग-अलग अवयव ({1,2,3,5,10,15}) होंगे।
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यदि \(A=\{1,2,5,7\}\), \(B=\{2,4,6\}\) और \(C=\{5,6,8\}\) हैं, तो (A\cap \(B\cup C\)) क्या है?
If \(A=\{1,2,5,7\}\), \(B=\{2,4,6\}\), and \(C=\{5,6,8\}\), what is (A\cap \(B\cup C\))?
#sets
#union
#intersection
#mixed
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A ( {2,5} )
B ( {1,7} )
C ( {2,4,5,6,8} )
D \( \varnothing \)
Explanation opens after your attempt
Correct Answer
A. ( {2,5} )
Step 1
Concept
First find \(B\cup C={2,4,5,6,8}\). Then the common elements with (A) are (2) and (5).
Step 2
Why this answer is correct
The correct answer is A. ( {2,5} ). First find \(B\cup C={2,4,5,6,8}\). Then the common elements with (A) are (2) and (5).
Step 3
Exam Tip
पहले \(B\cup C={2,4,5,6,8}\) निकालें। फिर (A) से सामान्य अवयव (2) और (5) मिलते हैं।
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यदि \(A=\{10,20,30,40\}\), \(B=\{20,50\}\) और \(C=\{30,60\}\) हैं, तो (A-\(B\cup C\)) क्या है?
If \(A=\{10,20,30,40\}\), \(B=\{20,50\}\), and \(C=\{30,60\}\), what is (A-\(B\cup C\))?
#sets
#difference
#union
#mixed
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A ( {10,40} )
B ( {20,30} )
C ( {50,60} )
D ( {10,20,30,40,50,60} )
Explanation opens after your attempt
Correct Answer
A. ( {10,40} )
Step 1
Concept
\(B\cup C={20,30,50,60}\). Removing (20) and (30) from (A) leaves ({10,40}).
Step 2
Why this answer is correct
The correct answer is A. ( {10,40} ). \(B\cup C={20,30,50,60}\). Removing (20) and (30) from (A) leaves ({10,40}).
Step 3
Exam Tip
\(B\cup C={20,30,50,60}\) है। (A) से (20) और (30) हटाने पर ({10,40}) बचता है।
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