In a factory 70% of the workers like oranges 64% like apples .if x% like both oranges and apples then

Solution: Let the total numberof workers be 100 . A , the set of workers who like orange and B, the set of workers who like apples.

So, $\\ n(A)=70, n(B)=64, n(A\cap B)=x$

Also

$n(A\cup B)\leq 100\\ \\\Rightarrow n(A)+n(B)-n(A\cap B)\leq 100\\ \\\Rightarrow 70+64-x\leq 100\Rightarrow x\geq 34$

Since

$\\ n(A\cap B)\leq n(B)\Rightarrow x\leq 64\\ \\\Rightarrow 34\leq x\leq 64$

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