Let A = \ x, y, z\ ~and~ B = \ 1, 2\ .~Find the number of relations...

Given :

$A = \left\{x, y, z\right\}$~and~$B = \left\{1, 2\right\}$

$⇒ A \times B = \left\{x, y, z\right\} \times \left\{1, 2\right\} = \left\{\left(x, 1\right), \left(x, 2\right), \left(y, 1\right), \left(y, 2\right), \left(z, 1\right), \left(z, 2\right)\right\}$

Since $n\left(A \times B\right) = 6$, so the number of all relations from~the set $A$~to set~$B = {2}^{6} = 64$&