Question

$AandB$are two sets $n(A-B)=8+2x,n(B-A)=6xandn(A\cap B)=x.Ifn\left(A\right)=n\left(B\right)thenn(A\cap B)=...$

• A. $26$
• B. $50$
• C. $24$
• D. none of these

Answer 1

The correct option is D

none of these

Explanation for the correct options:

Finding the value:

Let,$n(A\cap B)=x$

Here,$n(A–B)+n(B–A)=n\left(A\right)+n\left(B\right)–2n(A\cap B)$

$\Rightarrow$ $8+2x+6x=2n\left(A\right)–2x\left[\because n\left(A\right)=n\left(B\right)\right]$

$\Rightarrow$ $n\left(A\right)=4+5x$

Now, $n(A–B)=n\left(A\right)–n(A\cap B)$

$\Rightarrow$ $8+2x=4+5x$$-x$

$\Rightarrow$ $x=2$

$\Rightarrow$ $n(A\cap B)=2$

Hence, option(D) is correct.