Question

A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples then find the value of x.

Answer 1

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Let A be the set of Americans like cheese and B be the set of the Americans like apple.
n(A)=63,n(B)=76,andn(A∩B)=x∵n(A∪B)≤100⇒n(A)+n(B)−n( A n B)≤100⇒63+76−x≤100⇒x≥39Also,n(A∩B)≤min{n(A),n(B)}⇒x≤63∴39≤x≤63