\(यदि (U={1,2,\ldots,84}), (A={x:x\) 12 से विभाज्य है\(}) और (B={x:x\) 21 से विभाज्य है\(}), तो (|(A\cap B)'|) कितना है\)?
\(If (U={1,2,\ldots,84}), (A={x:x\) is divisible by \(12}) and (B={x:x\) is divisible by \(21}), what is (|(A\cap B)'|)\)?
Explanation opens after your attempt
Correct Answer
B. (83)
Concept
\(A\cap B\) contains multiples of (\operatorname{lcm}(12,21)=84), so only (84) appears. Hence the complement has (84-1=83) elements.
Why this answer is correct
The correct answer is B. (83). \(A\cap B\) contains multiples of (\operatorname{lcm}(12,21)=84), so only (84) appears. Hence the complement has (84-1=83) elements.
Exam Tip
\(A\cap B\) में (\operatorname{lcm}(12,21)=84) के गुणज हैं, इसलिए केवल (84) आता है। अतः पूरक में (84-1=83) अवयव हैं।
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