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 481-490 of 600 questions.
If \(A-B=A \cap B'\), what is ((A-B)') equal to?
A. \(A' \cup B\)
((A-B)'=\(A \cap B'\)'=A' \cup (B')') होता है। इसलिए उत्तर \(A' \cup B\) है। / ((A-B)'=\(A \cap B'\)'=A' \cup (B')'). Therefore the answer is \(A' \cup B\).
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If \(U=\mathbb{R}\), (A=\(-\infty,1\)), and (B=\(4,\infty\)), what is (\(A \cup B\)')?
A. ([1,4])
\(A \cup B\) में (1) और (4) शामिल नहीं हैं। इसलिए पूरक में दोनों सिरों सहित ([1,4]) आएगा। / The set \(A \cup B\) does not include (1) and (4). Hence the complement includes both endpoints, giving ([1,4]).
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Which statement is false for the complement of (A)?
A. (A') सार्वत्रिक समुच्चय से स्वतंत्र होता है(A') is independent of the universal set
पूरक सार्वत्रिक समुच्चय पर निर्भर करता है। इसलिए (A') को (U) बताए बिना निश्चित नहीं किया जा सकता। / The complement depends on the universal set. So (A') cannot be fixed without knowing (U).
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\(If (U={1,2,\ldots,16}) and (A={x:x \in U\) and 4 is a divisor of x}), what is (A')?
A. ({1,2,3,5,6,7,9,10,11,13,14,15})
(A) में (4) के गुणज ({4,8,12,16}) हैं। बाकी सभी सदस्य (A') में होंगे। / (A) contains the multiples of (4), namely ({4,8,12,16}). All remaining elements belong to (A').
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If \(A \subseteq U\), what is ((U-A)') equal to?
A. (A)
(U-A=A') होता है। इसलिए ((U-A)'=(A')'=A) है। / (U-A=A'). Therefore ((U-A)'=(A')'=A).
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A. (55)
\(A \cap B\) में (12) के गुणज होंगे और (60) तक ऐसे (5) हैं। इसलिए पूरक (60-5=55) है। / \(A \cap B\) contains multiples of (12), and there are (5) up to (60). Hence the complement is (60-5=55).
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If \(U={1,2,\ldots,8}\), \(A=\{1,2,5\}\), and \(B=\{2,4,6\}\), what is \(A' \cup B'\)?
A. ({1,3,4,5,6,7,8})
डी मॉर्गन से (A' \cup B'=\(A \cap B\)') है। \(A \cap B={2}\), इसलिए पूरक ({1,3,4,5,6,7,8}) है। / By De Morgan, (A' \cup B'=\(A \cap B\)'). Since \(A \cap B={2}\), the complement is ({1,3,4,5,6,7,8}).
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If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R}, -1<x\le 6}\), what is (A')?
A. ((-\infty,-1] \cup \(6,\infty\))
(-1) (A) में नहीं है इसलिए पूरक में शामिल है, जबकि (6) (A) में है इसलिए पूरक में नहीं है। / The point (-1) is not in (A), so it is included in the complement, while (6) is in (A), so it is excluded.
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\(If (U={1,2,\ldots,25}), (A={x:x \in U\) and x is not prime}), what is (A')?
A. ({2,3,5,7,11,13,17,19,23})
यदि (A) में अभाज्य नहीं संख्याएं हैं, तो (A') में अभाज्य संख्याएं होंगी। (1) अभाज्य नहीं है। / If (A) contains non-prime numbers, then (A') contains prime numbers. Remember that (1) is not prime.
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If (A) and (B) satisfy \(A \cup B=U\), which statement about (A') is correct?
A. \(A' \subseteq B\)
जो सदस्य (A) में नहीं हैं, वे \(A \cup B=U\) के कारण (B) में होने चाहिए। इसलिए \(A' \subseteq B\) है। / Elements not in (A) must be in (B) because \(A \cup B=U\). Hence \(A' \subseteq B\).
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