Let A and B be two sets such that
Question:

Let $A$ and $B$ be two sets such that $n(A)=5, n(B)=3$ and $n(A \cap B)=2$.

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

(ii) $n(A \times B)$

(iii) $n(A \times B) \cap(B \times A)$

Solution:

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

$=5+3-2$

$=6$

(ii) $n(A \times B)=n(A) \times n(B)$

$=5 \times 3$

$=15$

(iii) $n(A \times B) \cap(B \times A)=n(A \times B)+n(B \times A)-$