# Let A and B be two sets such that n(A) = 3 and n (B) = 2.

Question:

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

Solution:

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 × B

B = Set of second elements of the ordered pair elements of A × B.

∴ xy, 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 $B=\{1,2\}$.