Question

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

Answer 1

We have,

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

$\therefore B\cup C=\{4,5\}\cup \{5,6\}$

$=\{4,5,6\}$

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

Now,

$A\times B=\{2,3\}\times \{4,5\}$

$=\left\{\right(2,4),(2,5),(3,4),(3,5\left)\right\}$

and, $A\times C=\{2,3\}\times \{5,6\}$

$=\left\{\right(2,5),(2,6),(3,5),(3,6\left)\right\}$

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