Question

Let A = {1, 2} and B = {3, 4}, write $A\times B.$ How many sub sets will $A\times B$ have? List them.

Answer 1

Here A = {1, 2} and B = {3, 4}

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

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

Number of elements in $A\times B=4$

$\therefore$ Number of subsets in $A\times B=2^4=16$

The subsets are:

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

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

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

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

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