Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 171-180 of 600 questions.
A. ({5,6,7,8,9})
न्यूनतम (B) वही होगा जो \(A^c\) है। यहां \(A^c={5,6,7,8,9}\) है। / The smallest (B) will be exactly \(A^c\). Here \(A^c={5,6,7,8,9}\).
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If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2,3\}\), which (B) makes \(B=A^c\) true?
A. ({4,5,6})
\(A^c\) में (U) के वे तत्व होंगे जो (A) में नहीं हैं। इसलिए \(B=\{4,5,6\}\) चाहिए। / \(A^c\) contains the elements of (U) that are not in (A). Therefore \(B=\{4,5,6\}\) is needed.
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If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,d,f\}\), which statement is correct?
A. \(B=A^c\)
(A) और (B) असंबद्ध हैं और दोनों मिलकर (U) बनाते हैं। इसलिए (B), (A) का पूरक है। / (A) and (B) are disjoint and together form (U). Therefore (B) is the complement of (A).
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If \(A\cap B=\varnothing\) and \(A\cup B=U\), then (B) is equal to what?
A. \(A^c\)
यदि दो समुच्चय असंबद्ध हों और मिलकर (U) बनाएं, तो वे एक-दूसरे के पूरक होते हैं। इसलिए \(B=A^c\) होगा। / If two sets are disjoint and together form (U), then they are complements of each other. Hence \(B=A^c\).
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If \(A\cup A^c=U\) and \(A\cap A^c=\varnothing\), then (n(A)+n\(A^c\)) is equal to what?
A. (n(U))
(A) और \(A^c\) असंबद्ध हैं और मिलकर (U) बनाते हैं। इसलिए उनकी संख्याओं का योग (n(U)) होता है। / (A) and \(A^c\) are disjoint and together form (U). Therefore the sum of their cardinalities is (n(U)).
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If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\), what is (\(A^c\)^c\cap{2,4,6,8})?
A. ({2,4})
(\(A^c\)^c=A) होता है। इसलिए \(A\cap{2,4,6,8}={2,4}\) है। / (\(A^c\)^c=A). Therefore \(A\cap{2,4,6,8}={2,4}\).
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If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{2,5,8\}\), how many elements are in \(A^c\cup{5}\)?
A. (8)
\(A^c\) में (7) तत्व हैं क्योंकि (A) में (3) तत्व हैं। (5) \(A^c\) में नहीं है, इसलिए जोड़ने पर संख्या (8) होगी। / \(A^c\) has (7) elements because (A) has (3) elements. Since (5) is not in \(A^c\), adding it makes the count (8).
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If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{2,4,6\}\), what is \(A^c-{1,3,5}\)?
A. ({7,8,9})
\(A^c={1,3,5,7,8,9}\) है। इसमें से ({1,3,5}) हटाने पर ({7,8,9}) मिलता है। / \(A^c={1,3,5,7,8,9}\). Removing ({1,3,5}) gives ({7,8,9}).
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\(If (U={x:x\) is a digit\(}) and (A={x:x\) is an even digit\(}), how many elements are in (A^c)\)?
A. (5)
अंकों का \(U=\{0,1,2,3,4,5,6,7,8,9\}\) है। सम अंक (5) हैं, इसलिए विषम अंक भी (5) हैं। / The digit set is \(U=\{0,1,2,3,4,5,6,7,8,9\}\). There are (5) even digits, so there are (5) odd digits.
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A. ({1,2,3,4,5,7,8,9,10,11})
दोनों से विभाज्य होने का अर्थ (6) से विभाज्य होना है, इसलिए \(A=\{6,12\}\)। बाकी तत्व \(A^c\) हैं। / Divisible by both means divisible by (6), so \(A=\{6,12\}\). The remaining elements are \(A^c\).
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