Question

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

Answer 1

Given, $A=\{1,2,3\},B=\{3,4\},C=\{4,5,6\}$
$\Rightarrow A\cup (B\cup C)=\{1,2,3,4,5,6\}$

Now $A\times B=\{(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)\}$

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

Hence $(A\times B)\cap (B\times C)=\left\{(3,4)\right\}.$