\(यदि (U={1,2,\ldots,84}), (A={x:x\) 6 से विभाज्य है\(}) और (B={x:x\) 14 से विभाज्य है\(}), तो (|(A\cap B)'|) कितना है\)?
\(If (U={1,2,\ldots,84}), (A={x:x\) is divisible by \(6}) and (B={x:x\) is divisible by \(14}), what is (|(A\cap B)'|)\)?
Explanation opens after your attempt
Correct Answer
C. (82)
Concept
\(A\cap B\) contains multiples of (\operatorname{lcm}(6,14)=42), namely ({42,84}). Therefore (|\(A\cap B\)'|=84-2=82).
Why this answer is correct
The correct answer is C. (82). \(A\cap B\) contains multiples of (\operatorname{lcm}(6,14)=42), namely ({42,84}). Therefore (|\(A\cap B\)'|=84-2=82).
Exam Tip
\(A\cap B\) में (\operatorname{lcm}(6,14)=42) के गुणज हैं, यानी ({42,84})। इसलिए (|\(A\cap B\)'|=84-2=82)।
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