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  4. If n(A)=43, n(B)=51 and n(A∪ B)=75, then n(A-B)∪(B-A) is equal to

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Q. If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to

KEAMKEAM 2013Sets

Solution:

Given, $n(A)=43, \,n(B)=51$ and $n(A \cup B)=75$
Now, by addition theorem of probability,
$n(A \cap B) =n(A)+n(B)-n(A \cup B) $
$=43+51-75=19 $
Now, $n[(A-B) \cup(B-A)] $
$=n(A \cup B)-n(A \cap B) $
$=75-19=56$