Question

Given A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find $(A\times B)\cap (B\times C).$

Answer 1

We have,

A = {1, 2, 3} B = {3, 4} and C = {4, 5, 6}

$\therefore A\times B=\{1,2,3\}\times \{3,4\}$

$=\left\{\right(1,3),(1,4),(2,3),(2,4),(3,3),(3,4\left)\right\}$

and, $B\times C=\{3,4\}\times \{4,5,6\}$

$=\left\{\right(3,4),(3,5),(3,6),(4,4),(4,5),(4,6\left)\right\}$

$\therefore (A\times B)\cap (B\times C)=\{3,4\}$