Question

In a universal set x,$n\left(x\right)=50$ ,$n\left(A\right)=35$ , $n\left(B\right)=20$ , $n\left(A^{\prime }\cap B^{\prime }\right)=5$ ,then $n\left(A\cup B\right),n\left(A\cap B\right)$ are repsectively

• A. $45,10$
• B. $10,45$
• C. $25,30$
• D. $15,25$

Answer 1

The correct option is A $45,10$

Given $n\left(X\right)=50$,

$n\left(A\right)=35$,

$n\left(B\right)=20$

$n(A^{\prime }\cap B^{\prime })=5$

$\left(i\right)n(A\cup B)$

$n(A^{\prime }\cap B^{\prime })=n\left(X\right)-n(A\cup B)$

$n(A\cup B)=n\left(X\right)-n(A^{\prime }\cap B^{\prime })$

$n(A\cup B)=50-5=45$

$\left(ii\right)n(A\cap B)$

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$n(A\cap B)=35+20-45=10$