$(20$ points$)$

Suppose $g$:$AB$ and $f$:$BC$ where $A=\{1,2,3,4\},B=\{a,b,c\},C=\{2,7,10\},$ and $f$ and $g$ are defined by $g=\{(1,b),(2,a),(3,a),(4,b)\}$ and $f=\{(a,10),(b,7),(c,2)\}.$