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Q.
A survey shows that $63\%$ of the people watch a News Channel whereas $76\%$ watch another channel. If $x\%$ of the people watch both channel, then
Sets
Solution:
Let $A$ and $B$ be the two sets of news channel such that
$n(A) = 63$, $n(B) = 76$, $n(A \cup B) = 100$
Also, $n (A \cap B) = x$
Using, $n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$\Rightarrow 100 = 63 + 76 - x$
$\Rightarrow x = 139 - 100 = 39$
Again $n(A \cap B) \le n(A)$
$\Rightarrow x \le 63$
$\therefore 39 \le x \le 63$