Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 141-150 of 588 questions.
If \(U=\{2,4,6,8,10\}\) and \(A=\{2,10\}\), what is ((A')')?
A. ({2,10})
पूरक का पूरक मूल समुच्चय होता है। इसलिए ((A')'=A={2,10}) है। / The complement of a complement is the original set. Hence ((A')'=A={2,10}).
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If \(A=\{1,3,9\}\), how many subsets in (\mathcal{P}(A)) will include ({1,9})?
B. (2)
(1) और (9) रखना तय है और (3) को लेने या न लेने के (2) तरीके हैं। इसलिए ऐसे (2) उपसमुच्चय हैं। / Keeping (1) and (9) is fixed and (3) can be taken or not taken in (2) ways. So there are (2) such subsets.
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If \(U=\{all one digit natural numbers\}\) and \(A=\{2,4,6,8\}\), what is (A')?
A. ({1,3,5,7,9})
एक अंकीय प्राकृतिक संख्याएं (1) से (9) तक हैं। (A) हटाने पर (1,3,5,7,9) बचते हैं। / One digit natural numbers are from (1) to (9). After removing (A), (1,3,5,7,9) remain.
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If \(A=\{1,2,3,4\}\), how many subsets in (\mathcal{P}(A)) contain (2) and do not contain (3)?
B. (4)
(2) लेना और (3) न लेना तय है। बाकी (1,4) के लिए \(2^2=4\) विकल्प हैं। / Taking (2) and not taking (3) are fixed. For remaining (1,4), there are \(2^2=4\) choices.
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If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,5,7\}\) and (B=A'), what is (B')?
A. ({2,5,7})
यदि (B=A') है तो (B'=(A')'=A) होगा। इसलिए (B'={2,5,7}) है। / If (B=A'), then (B'=(A')'=A). Therefore (B'={2,5,7}).
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If \(A={\emptyset,{\emptyset},0}\), what is (n(\mathcal{P}(A)))?
C. (8)
(A) में तीन अलग तत्व \(\emptyset,{\emptyset},0\) हैं। इसलिए (n(\mathcal{P}(A))=23=8) है। / (A) has three distinct elements \(\emptyset,{\emptyset},0\). Therefore (n(\mathcal{P}(A))=23=8).
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If \(U=\{5,10,15,20,25,30\}\) and \(A=\{10,20,30\}\), what is (A')?
A. ({5,15,25})
(U) से (10,20,30) हटाने पर (5,15,25) बचते हैं। यही पूरक है। / After removing (10,20,30) from (U), (5,15,25) remain. This is the complement.
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B. (16) और (6)(16) and (6)
चार तत्वों वाले समुच्चय के कुल \(2^4=16\) उपसमुच्चय होते हैं। दो तत्व वाले उपसमुच्चय (6) होते हैं। / A set with four elements has \(2^4=16\) total subsets. The number of two element subsets is (6).
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If \(A=\{a,b,c\}\), how many subsets in (\mathcal{P}(A)) contain at least one of (a) or (b)?
C. (6)
कुल (8) उपसमुच्चय हैं और (a,b) दोनों को न रखने वाले (2) हैं। इसलिए (8-2=6) उपसमुच्चय सही हैं। / There are (8) total subsets and (2) subsets contain neither (a) nor (b). So (8-2=6) subsets are correct.
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If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,6\}\), what is \(A'\cap A\)?
C. \(\emptyset\)
कोई तत्व (A) और उसके पूरक (A') दोनों में नहीं हो सकता। इसलिए \(A'\cap A=\emptyset\) है। / No element can be in both (A) and its complement (A'). Therefore \(A'\cap A=\emptyset\).
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