Question:
Let $A$ and $B$ be two sets such that : $n(A)=20, n(A \cup B)=42$ and $n(A \cap B)=4$. Find
(i) $n(B)$
(ii) $n(A-B)$
(iii) $n(B-A)$
Solution:
Given:
$n(A)=20, n(A \cup B)=42$ and $n(A \cap B)=4$
(i) We know :
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$\Rightarrow 42=20+n(B)-4$
$\Rightarrow n(B)=26$
(ii) $n(A-B)=n(A)-n(A \cap B)$
$\Rightarrow n(A-B)=20-4=16$
(iii) We know that sets follow the commutative property.
$\therefore n(A \cap B)=n(B \cap A)$
$n(B-A)=n(B)-n(B \cap A)$
$\Rightarrow n(B-A)=26-4=22$