Question

Let $A$ and $B$ be two sets such that $n\left(A\right)=3$ and $n\left(B\right)=2$. If $(x,1),(y,2),(z,1)$ are in $A\times B$, then find $A$ and $B$, where $x,y,z$ are distinct elements.

Answer 1

Given:
$n\left(A\right)=3$ and $n\left(B\right)=2$; and $(x,1),(y,2),(z,1)$ are in $A\times B$.

Apply cartesian product of two sets
As we know,
$A=$ Set of first elements of the ordered pair elements of $A\times B$
$B=$ set of second elements of the ordered pair elements of $A\times B$
So, it is clear that set $A=$ {$x,y,z$} and set $B=$ {$1,2$}.