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 a value of x can be

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 a value of x can be

Infinity Learn · Accepted Answer

Let A denote the set of Americans who like cheese and let B denote the set of Americans who like apples. Let population of America be $$100$$.  Then $$n(A)=63$$,$$n(B)=76$$ Now, $$n(A$$∪$$B)=n(A)+n(B)$$−$$n(A$$∩$$B)=63+76$$−$$n(A$$∩$$B)$$⇒ $$n(A$$∩$$B)=139$$−$$n(A$$∪$$B)$$ But $$n(A$$∪$$B)$$≤$$100$$∴ $$139$$−$$n(A$$∪$$B)$$≥$$139$$−$$100=39$$∴ $$n(A$$∩$$B)$$≥$$39$$ i.e., $$39$$≤$$n(A$$∩$$B)$$ Again, A∩B⊆A,A∩B⊆B∴ $$n(A$$∩$$B)$$≤$$n(A)=63$$ and $$n(A$$∩$$B)$$≤$$n(B)=76$$∴ $$n(A$$∩$$B)$$≤$$63$$ Then, $$39$$≤$$n(A$$∩$$B)$$≤$$n(B)$$⇒$$39$$≤x≤$$63$$

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 a value of x can be

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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 a value of x can be

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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 a value of x can be