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.

Answer 1

Here $(x,1)ϵA\times B\Rightarrow xϵA$ and $1ϵB$

$(y,2)ϵA\times B\Rightarrow yϵA$ and $2ϵB$

$(z,1)ϵA\times B\Rightarrow zϵA$ and $1ϵB$

It is given that n (A) = 3 and n(B) = 2

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

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