Question

If $n\left(A\right)=n\left(B\right),$ then which of the following is correct?

• A. $n(A–B)=n(B–A)$
• B. $n(A\cup B)=n\left(A\right)+n\left(B\right)$
• C. $n(A\cap B)=n\left(B\right)+n(A–B)$
• D. $n(A–B)=n(A\cap B)$

Answer 1

The correct option is A $n(A–B)=n(B–A)$

Let us assume $A=\{a,b,c,d\}$ and $B=\{c,d,e,f\}$.
$n\left(A\right)=n\left(B\right)=4$
Drawing the venn diagram of these sets
We observe that,
$n(A–B)=n(B–A)=2$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$
$n(A–B)=n\left(A\right)-n(A\cap B)$