\(यदि (U={1,2,\ldots,60}), (A={x:x\) 6 से विभाज्य है\(}) और (B={x:x\) 10 से विभाज्य है\(}), तो (|(A\cap B)'|) कितना है\)?
\(If (U={1,2,\ldots,60}), (A={x:x\) is divisible by \(6}) and (B={x:x\) is divisible by \(10}), what is (|(A\cap B)'|)\)?
Explanation opens after your attempt
Correct Answer
C. (58)
Concept
\(A\cap B\) contains multiples of (\operatorname{lcm}(6,10)=30), namely (30,60). Hence the complement has (60-2=58) elements.
Why this answer is correct
The correct answer is C. (58). \(A\cap B\) contains multiples of (\operatorname{lcm}(6,10)=30), namely (30,60). Hence the complement has (60-2=58) elements.
Exam Tip
\(A\cap B\) में (\operatorname{lcm}(6,10)=30) के गुणज हैं, यानी (30,60)। इसलिए पूरक में (60-2=58) अवयव हैं।
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