Question

A and B are two overlapping sets such that n(A $\cap$ B) = x + 4, n(A - B) = 4x - 8 and n(B) = 3x + 8. Find x, if n(A $\cup$ B) = 70.

Answer 1

Given, $n(A\cap B)=x+4,n(A-B)=4x-8,n\left(B\right)=3x+8$

Also given $n(A\cup B)=70$

We know that $n(A-B)=n(A\cup B)-n\left(B\right)$
Substituting the given values, we get
$4x-8=70-3x-8$
$\Rightarrow 7x=70$
$\Rightarrow x=10$