COMP 2711 Ex 4

1

There are $3^2=9$ functions

$$\begin{array}{rlrl}& f(1)=a& & f(2)=a\\ & f(1)=a& & f(2)=b\\ & f(1)=a& & f(2)=c\\ & f(1)=b& & f(2)=a\\ & f(1)=b& & f(2)=b\\ & f(1)=b& & f(2)=c\\ & f(1)=c& & f(2)=a\\ & f(1)=c& & f(2)=b\\ & f(1)=c& & f(2)=c\end{array}$$

2

There are $2^3=8$ functions

$$\begin{array}{rlrlrl}& f(1)=a& & f(2)=a& & f(3)=a\\ & f(1)=a& & f(2)=a& & f(3)=b\\ & f(1)=a& & f(2)=b& & f(3)=a\\ & f(1)=a& & f(2)=b& & f(3)=b\\ & f(1)=b& & f(2)=a& & f(3)=a\\ & f(1)=b& & f(2)=a& & f(3)=b\\ & f(1)=b& & f(2)=b& & f(3)=a\\ & f(1)=b& & f(2)=b& & f(3)=b\end{array}$$