यदि (n(A)=4), (n(B)=5) और (n\(A\cap B\)=2), तो (n(\(A\cap B\)\times\(A\cup B\))) कितना है?
If (n(A)=4), (n(B)=5), and (n\(A\cap B\)=2), what is (n(\(A\cap B\)\times\(A\cup B\)))?
#cartesian-product
#union-intersection
#cardinality
A (10)
B (12)
C (14)
D (18)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=4+5-2=7) and (n\(A\cap B\)=2). Hence the total is \(2\cdot7=14\).
Step 2
Why this answer is correct
The correct answer is C. (14). (n\(A\cup B\)=4+5-2=7) and (n\(A\cap B\)=2). Hence the total is \(2\cdot7=14\).
Step 3
Exam Tip
(n\(A\cup B\)=4+5-2=7) और (n\(A\cap B\)=2)। इसलिए कुल \(2\cdot7=14\) है।
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यदि \(A\subseteq U\), तो \(A\cup A'\) और \(A\cap A'\) क्रमशः क्या हैं?
If \(A\subseteq U\), what are \(A\cup A'\) and \(A\cap A'\) respectively?
#sets
#complement
#identity
#union-intersection
A \(U,\varnothing\)
B \(\varnothing,U)
C (A,U)
D (A',A)
Explanation opens after your attempt
Correct Answer
A. \(U,\varnothing\)
Step 1
Concept
(A) and (A') together make the whole (U), and their common part is empty. This is the paired identity of complement.
Step 2
Why this answer is correct
The correct answer is A. \(U,\varnothing\). (A) and (A') together make the whole (U), and their common part is empty. This is the paired identity of complement.
Step 3
Exam Tip
(A) और (A') मिलकर पूरा (U) बनाते हैं तथा उनका साझा भाग रिक्त होता है। यह पूरक की जोड़ी पहचान है।
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यदि (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)) है, तो यह कौन-सा नियम है?
If (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)), which law is this?
#sets
#identity
#distributive-law
#union-intersection
A वितरण नियम / Distributive law
B क्रमविनिमेय नियम / Commutative law
C सहचर नियम / Associative law
D पूरक नियम / Complement law
Explanation opens after your attempt
Correct Answer
A. वितरण नियम / Distributive law
Step 1
Concept
This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.
Step 2
Why this answer is correct
The correct answer is A. वितरण नियम / Distributive law. This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.
Step 3
Exam Tip
यह प्रतिच्छेद का संघ पर वितरण है। पहचान वाले प्रश्नों में प्रतीकों की स्थिति ध्यान से देखें।
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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
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 \(A=\{1,2,4,6,8\}\), \(B=\{2,3,6,9\}\) और \(C=\{6,8,10\}\) हैं, तो (\(A\cup B\)\cap C) क्या है?
If \(A=\{1,2,4,6,8\}\), \(B=\{2,3,6,9\}\), and \(C=\{6,8,10\}\), what is (\(A\cup B\)\cap C)?
#sets
#mixed-operation
#union-intersection
A ( {6,8} )
B ( {2,6} )
C ( {10} )
D ( {1,2,3,4,6,8,9,10} )
Explanation opens after your attempt
Correct Answer
A. ( {6,8} )
Step 1
Concept
\(A\cup B={1,2,3,4,6,8,9}\). Its intersection with (C) is ({6,8}).
Step 2
Why this answer is correct
The correct answer is A. ( {6,8} ). \(A\cup B={1,2,3,4,6,8,9}\). Its intersection with (C) is ({6,8}).
Step 3
Exam Tip
\(A\cup B={1,2,3,4,6,8,9}\) है। इसका (C) से प्रतिच्छेद ({6,8}) है।
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यदि \(A=\{r,s,t,u\}\), \(B=\{s,u,v\}\) और \(C=\{u,v,w\}\) हैं, तो (A\cap\(B\cup C\)) क्या है?
If \(A=\{r,s,t,u\}\), \(B=\{s,u,v\}\), and \(C=\{u,v,w\}\), what is (A\cap\(B\cup C\))?
#sets
#mixed-operation
#union-intersection
A ( {s,u} )
B ( {r,t} )
C ( {u,v} )
D ( {r,s,t,u,v,w} )
Explanation opens after your attempt
Correct Answer
A. ( {s,u} )
Step 1
Concept
First \(B\cup C={s,u,v,w}\). Its common part with (A) is ({s,u}).
Step 2
Why this answer is correct
The correct answer is A. ( {s,u} ). First \(B\cup C={s,u,v,w}\). Its common part with (A) is ({s,u}).
Step 3
Exam Tip
पहले \(B\cup C={s,u,v,w}\) है। इसका (A) से सामान्य भाग ({s,u}) है।
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यदि \(A\cup B=A\) और \(A\cap B=B\) है, तो सही संबंध कौन सा है?
If \(A\cup B=A\) and \(A\cap B=B\), which relation is correct?
#sets
#subset
#union-intersection
A \(B\subseteq A\)
B \(A\subseteq B\)
C \(A=B=\emptyset\)
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Correct Answer
A. \(B\subseteq A\)
Step 1
Concept
Both conditions show that every element of (B) is in (A). Therefore \(B\subseteq A\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(B\subseteq A\). Both conditions show that every element of (B) is in (A). Therefore \(B\subseteq A\) is correct.
Step 3
Exam Tip
दोनों स्थितियां बताती हैं कि (B) के सभी अवयव (A) में हैं। इसलिए \(B\subseteq A\) सही है।
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यदि \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\) और \(C=\{3,4,5\}\) हैं, तो (\(A\cap B\)\cup C) क्या है?
If \(A=\{2,3,5,7\}\), \(B=\{1,3,5,9\}\), and \(C=\{3,4,5\}\), what is (\(A\cap B\)\cup C)?
#sets
#mixed-operation
#union-intersection
A ( {3,5} )
B ( {3,4,5} )
C ( {2,3,4,5,7} )
D ( {1,2,3,4,5,7,9} )
Explanation opens after your attempt
Correct Answer
B. ( {3,4,5} )
Step 1
Concept
\(A\cap B={3,5}\), and union with (C) gives ( {3,4,5} ). Find the bracket result first.
Step 2
Why this answer is correct
The correct answer is B. ( {3,4,5} ). \(A\cap B={3,5}\), and union with (C) gives ( {3,4,5} ). Find the bracket result first.
Step 3
Exam Tip
\(A\cap B={3,5}\), और (C) से संघ लेने पर ( {3,4,5} ) मिलता है। पहले कोष्ठक का परिणाम निकालें।
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यदि \(A\subseteq B\), तो \(A\cup B\) और \(A\cap B\) क्रमशः क्या होंगे?
If \(A\subseteq B\), what are \(A\cup B\) and \(A\cap B\), respectively?
#sets
#venn-diagrams
#subset
#union-intersection
A (B) और (A) / (B) and (A)
B (A) और (B) / (A) and (B)
C (U) और \(\varnothing\) / (U) and \(\varnothing\)
D \(\varnothing\) और (U) / \(\varnothing\) and (U)
Explanation opens after your attempt
Correct Answer
A. (B) और (A) / (B) and (A)
Step 1
Concept
When \(A\subseteq B\), the union is (B) and the common part is (A). This is immediate from the subset Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. (B) और (A) / (B) and (A). When \(A\subseteq B\), the union is (B) and the common part is (A). This is immediate from the subset Venn diagram.
Step 3
Exam Tip
जब \(A\subseteq B\), तब मिलाकर (B) और साझा भाग (A) होता है। उपसमुच्चय वाले वेन आरेख में यह तुरंत दिखता है।
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