Question

How many of the relations from A to B are functions. If A = {$a$, $b$, $c$} and B = {$x$, $y$}, then R = { ($a$, $x$), ($c$, $x$) ($b$, $y$), ($a$, $y$)}

Answer 1

Given, $A=$ {$a,b,c$}, $B=$ {$x,y$}

A function is a set of ordered pairs in which each $x$-element from the first set has only ONE $y$-element from the second Set associated with it.
Since element $a$ of SET $A$ is associated with both $x,y$ of $B$, the given relation is not a function.