Let A= {x, y, z} and B = {a, b, c, d}. Which one of the following is not a relation from A to B?

$\mathrm{R}\subseteq \mathrm{A}\times \mathrm{B}$ For given $\mathrm{A}=\{\mathrm{x},\mathrm{y},\mathrm{z}\}$ and $B=\{a,b,c,d\}$

$A\times B=\left\{\begin{array}{r}(x,a),(x,b),(x,c),(x,d),(y,a),(y,b),\\ (y,c),(y,d),(z,a),(z,b),(z,c),(z,d)\end{array}\right\}$

Clearly, {(z, b), (y, b), (a, d)} is not the subset of Ax B.

$\therefore$ It is not a relation.