Let $X = \{ 1,2,3,4,5 \}$ And $Y = \{ u , v , w , x , y \}$

Essay

Let $X = \{ 1,2,3,4,5 \}$ and $Y = \{ u , v , w , x , y \}$ , and define $h : X \rightarrow Y$ as follows:
$h ( 1 ) = v , h ( 2 ) = x , h ( 3 ) = v , h ( 4 ) = v , h ( 5 ) = y .$
(a) Draw an arrow diagram for $h$ .
(b) Let $A = \{ 1,2 \} , C = \{ x , v \} , D = \{ w \}$ , and $E = \{ w , y \}$ . Find
$$h ( A ) , h ( X ) , h ^ { - 1 } ( C ) , h ^ { - 1 } ( D ) , h ^ { - 1 } ( E ) , \text { and } h ^ { - 1 } ( Y ) .$$