It is given that $n(A)=3$ and $n(B)=2 ;$ and $(x, 1),(y, 2),(z, 1)$ are in $A \times B$

We know that

$A=$ Set of first elements of the ordered pair elements of $A \times B$

$B =$ Set of second elements of the ordered pair elements of $A \times B$

$\therefore x, y,$ and $z$ are the elements of $A ;$ and $1$ and $2$ are the elements of $B$

Since $n(A)=3$ and $n(B)=2$

It is clear that $A=\{x, y, z\}$ and $B=\{1,2\}$