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  4. If n(μ) = 60 , n(A) = 21, n(B) = 43 then Least value of n (A∩ B) and Greatest value of n (A∩ B) are

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Q. If $n\left(\mu\right) = 60$ , $n\left(A\right) = 21$, $n\left(B\right) = 43$ then Least value of $n \left(A\cap B\right)$ and Greatest value of $n \left(A\cap B\right)$ are

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Solution:

$n\left(\mu\right) = 60, n\left(A\right) =21, n\left(B\right) =43$
Greatest value of $ n\left(A\cap B\right) =n\left(A\right) =21 $
$n\left(A\cup B\right) \le60$
$ \Rightarrow n\left(A\right) + n\left(B\right)-n\left(A\cap B\right) = 60 $
$\Rightarrow n\left(A \cap B\right)\ge21 + 43 - 60 = 4 $
Least value of $n\left(A \cap B\right)=4$