Exercise $4$:

Let $A=\{a,b,c\}$ and $B=\{a,b\}($with $a,b,c$ all different$).$ Give an example of:

$($a$)$ a function $f$ : A $->$ B that is not onto but where $f(a)b$

$($b$)$ a function $g$ : A $->$ B that is onto but where $g(a)=g(b)=a$

$($c$)$ a function $h$ : A $->$ B that is onto but $h(x)x$ for each xinB.

$($d$)$ a function i : $B$A that is one$-$to$-$one but $i(x)x$ for each xinB.