Let A and B be two sets such that :

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.

$\therefore n(A \cap B)=n(B \cap A)$

$n(B-A)=n(B)-n(B \cap A)$

$\Rightarrow n(B-A)=26-4=22$