Mapping/Value table/Composition/2/Exercise

We consider the sets

$L=\{1,2,3,4,5,6,7,8\},\,M=\{a,b,c,d,e,f,g,h,i\}{\text{ and }}N=\{R,S,T,U,V,W,X,Y,Z\}$

and the mappings ${}\varphi \colon L\rightarrow M$ and ${}\psi \colon M\rightarrow N$ which are given by the value tables

${}x$	${}1$	${}2$	${}3$	${}4$	${}5$	${}6$	${}7$	${}8$
${}\varphi (x)$	${}c$	${}i$	${}a$	${}g$	${}d$	${}e$	${}h$	${}b$

and

${}y$	${}a$	${}b$	${}c$	${}d$	${}e$	${}f$	${}g$	${}h$	${}i$
${}\psi (y)$	${}X$	${}Z$	${}Y$	${}S$	${}Z$	${}S$	${}T$	${}W$	${}U$

respectively.

1. Determine a value table for ${}\psi \circ \varphi$.
2. Are the mappings ${}\varphi$, ${}\psi$, ${}\psi \circ \varphi$ injective?
3. Are the mappings ${}\varphi$, ${}\psi$, ${}\psi \circ \varphi$ surjective?

Create a solution