A survey shows that 63% of the Americans like | vedclass

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Question

(c) Let $A$ denote the set of Americans who like cheese and let $B$ denote the set of Americans who like apples.

Let Population of American be $100

Vedclass · Accepted Answer

$39 \le x \le 63$

Vedclass · Answer

(c) Let $A$ denote the set of Americans who like cheese and let $B$ denote the set of Americans who like apples.

Let Population of American be $100$.

Then $n\,(A) = 63,n\,(B) = 76$

Now, $n\,(A \cup B) = n(A) + n(B) - n(A \cap B)$

$ = 63 + 76 - n(A \cap B)$

 $	herefore n\,(A \cup B) + n(A \cap B) = 139$

==> $n\,(A \cap B) = 139 - n(A \cup B)$

But $n\,(A \cup B) \le 100$

$	herefore - n\,(A \cup B) \ge - 100$

 $	herefore 139 - n\,(A \cup B) \ge 139 - 100 = 39$

 $	herefore n(A \cap B) \ge 39$ i.e., $39 \le n(A \cap B)$.....(i)

Again, $A \cap B \subseteq A,A \cap B \subseteq B$

$ 	herefore n\,(A \cap B) \le n\,(A) = 63$ and $n\,(A \cap B) \le n\,(B) = 76$

$	herefore n(A \cap B) \le 63$&hellip;..(ii)

Then, $39 \le n\,(A \cap B) \le 63$ ==> $39 \le x \le 63$.

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

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