Question

Given $A=2,3,B=4,5,C=5,6,$ find
(i) $A\times (B\cap C)=.......$
(ii) $(A\times B)\cup (B\times C)=.......$

Answer 1

(i) $B\cap C=5$

$A\times (B\cap C)=\left\{\right(2,5),(3,5\left)\right\}$
(ii) $(A\times B)=\left\{\right(2,4),(2,5),(3,4),(3,5\left)\right\}$

$(B\times C)=\left\{\right(4,5),(4,6),(5,5),(5,6\left)\right\}$

$(A\times B)\cup (B\times C)=\left\{\right(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,5),(5,6\left)\right\}$