Question

Let $A=\{1,2\}$ and $B=\{3,4\}$. Write $A\times B$ and find how many subsets will $A\times B$ have? List them.

Answer 1

$A=\{1,2\}$ and $B=\{3,4\}$
$\therefore A\times B=\left\{\right(1,3),(1,4),(2,3),(2,4\left)\right\}$
$\Rightarrow n(A\times B)=4$

We know that if $n(A\times B)=r$

Then, number of subsets of $A\times B$ is $2^r$
Therefore the set $A\times B$ has $2^4$ = $16$ subsets.

These are
$\varphi \left\{\right(1,3\left)\right\},\left\{\right(1,4\left)\right\},\left\{\right(2,3\left)\right\},\left\{\right(2,4\left)\right\},\left\{\right(1,3),(1,4\left)\right\},\left\{\right(1,3),(2,3\left)\right\},\left\{\right(1,3),(2,4\left)\right\},$

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

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