Question

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

Answer 1

Given:
$A=$ {$1,2$} and $B=$ {$3,4$}

Cartesian product of set $A$ and $B$
$A\times B=$ {$(1,3),(1,4),(2,3),(2,4)$}

Number of subsets of $A\times B$
Number of elements in $A\times B$ is $n(A\times B)=4$.
We know that,
If $C$ is set with $n\left(C\right)=m$, then $n\left[P\right(C\left)\right]=2^m$
Thus, the set $A\times B$ has $2^4=16$ subsets.

Finding list of subsets.
List of subsets is:
$\Phi$, {$(1,3)$}, {$(1,4)$}, {$(2,3)$}, {$(2,4)$}, {$(1,3),(1,4)$}, {$(1,4),(2,3)$}, {$(2,3),(2,4)$}, {$(2,4),(1,3)$}, {$(1,3),(2,3)$}, {$(1,4),(2,4)$}, {$(1,3),(1,4),(2,3)$}, {$(1,4),(2,3),(2,4)$}, {$(2,3),(2,4),(1,3)$}, {$(2,4),(1,3),(1,4)$}, {$(1,3),(1,4),(2,4),(2,3)$}.