Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 241-250 of 571 questions.
How many elements are there in (\mathcal{P}(\mathcal{P}({a})))?
B. (4)
(\mathcal{P}({a})) में (2) तत्व होते हैं। इसलिए उसके घात समुच्चय में \(2^2=4\) तत्व होंगे। / (\mathcal{P}({a})) has (2) elements. Therefore its power set has \(2^2=4\) elements.
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If \(U=\{a,b,c,d,e,f\}\) and \(A=\{a,c,f\}\), what is (A')?
A. ({b,d,e})
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां वे तत्व (b,d,e) हैं। / (A') contains elements of (U) that are not in (A). Here those elements are (b,d,e).
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If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{1,4,9\}\), how many elements will (A') have?
C. (7)
(U) में (10) और (A) में (3) तत्व हैं। अतः (n(A')=10-3=7)। / (U) has (10) elements and (A) has (3) elements. Hence (n(A')=10-3=7).
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B. (25)
(n\(A\cup B\)=32+28-10=50) होगा। किसी में नहीं (75-50=25) विद्यार्थी हैं। / (n\(A\cup B\)=32+28-10=50). Students in neither activity are (75-50=25).
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If (A) and (B) are subsets of (U), what is (\(A\cap B\)') equal to?
B. \(A'\cup B'\)
डी मॉर्गन नियम के अनुसार (\(A\cap B\)'=A'\cup B')। प्रतिच्छेद के पूरक में कम से कम एक समुच्चय से बाहर वाले तत्व आते हैं। / By De Morgan's law, (\(A\cap B\)'=A'\cup B'). The complement of an intersection includes elements outside at least one set.
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If \(A\subseteq U\) and \(A'= \varnothing\), which conclusion is correct?
B. (A=U)
पूरक खाली है तो (U) में (A) के बाहर कोई तत्व नहीं है। इसलिए (A=U) होगा। / If the complement is empty, no element of (U) lies outside (A). Therefore (A=U).
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If (n(U)=80) and (n(A')=19), what is (n(A))?
C. (61)
(A) और (A') मिलकर पूरा (U) बनाते हैं। इसलिए (n(A)=80-19=61)। / (A) and (A') together form the whole (U). So (n(A)=80-19=61).
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If \(A={x:x\) is a positive divisor of (24)(}), what is (n(\mathcal{P}(A)))?
C. (256)
(24) के भाजक (1,2,3,4,6,8,12,24) हैं इसलिए (n(A)=8)। अतः (n(\mathcal{P}(A))=28=256)। / The divisors of (24) are (1,2,3,4,6,8,12,24), so (n(A)=8). Hence (n(\mathcal{P}(A))=28=256).
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If \(A=\{k\}\), which is (\mathcal{P}(A))?
C. \({\varnothing,{k}}\)
एकल समुच्चय के उपसमुच्चय \(\varnothing\) और वही समुच्चय होते हैं। इसलिए घात समुच्चय में ({k}) आएगा, केवल (k) नहीं। / The subsets of a singleton set are \(\varnothing\) and the set itself. So the power set contains ({k}), not just (k).
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If \({m,n}\in \mathcal{P}(A)\), which statement is definitely true?
A. \(m\in A\) और \(n\in A\)\(m\in A\) and \(n\in A\)
\({m,n}\in \mathcal{P}(A)\) का अर्थ है \({m,n}\subseteq A\)। इसलिए (m) और (n) दोनों (A) के तत्व होंगे। / \({m,n}\in \mathcal{P}(A)\) means \({m,n}\subseteq A\). Therefore both (m) and (n) are elements of (A).
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