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,z are distinct elements.

Answer 1

Since (x, 1), (y, 2), (z, 1) are elements of $A\times B.$ Therefore, $x,y,zϵA$ and $1,2ϵB$ It is given that n(A) = 3 and n(B) = 2

$\therefore x,y,zϵA$ and n(A) = 3

$\Rightarrow A=\{x,y,z\}$

$1,2ϵB$ and n(B) = 2

$\Rightarrow B=\{1,2\}$