Question

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

Answer 1

We have $A=\{1,2,3\}$ and $B=\{3,4\}$

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

We have $A=\{1,2,3\}$ and $C=\{1,3,5\}$

$A\times C=\{(1,1),(1,3),(1,5),(2,1),(2,3),(2,5),(3,1),(3,3),(3,5),\}$

Now,$(A\times B)\cap (A\times C)$

$=\{(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)\}\cap \{(1,1),(1,3),(1,5),(2,1),(2,3),(2,5),(3,1),(3,3),(3,5),\}$

$=\{(1,3),(2,3),(3,3)\}$