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 $A\times B$ find $A$ and $B$ where $x,y$ and $z$ are distinct elements

Answer 1

It is given that $n\left(A\right)=3$ and $n\left(B\right)=2$ 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 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 $n\left(A\right)=3$ and $n\left(B\right)=2$ it is clear that $A=\{x,y,z\}$ and $B=\{1,2\}$