
\problemdata     
{S01-PS3-6}           
{relations}              
{Velleman Sec 4.2, Exercise 3 parts a,b and c}              
{F00-3, S01-PS3} 		
{S01 Karger}        	


\begin{problem} Suppose $A=\{1,2,3\}, B=\{4,5,6\}, R=\{(1,4), (1,5), (2,5),
(3,6)\}$, and $S=\{(4,5), (4,6), (5,4), (6,6)\}.$ Note that $R$ is a
relation from $A$ to $B$ and
$S$ is a relation from $B$ to $B$.  Find the following relations:\\
\medskip
a. $S\circ R$\\
b. $S\circ S$\\
c. $S^{-1}\circ R$

\solution{
a. $S\circ R = \{(1,5), (1,6), (1,4), (2,4), (3,6)\}$\\
b. $S\circ S = \{(4,4), (4,6), (5,5), (5,6), (6,6)\}$\\
c. $S^{-1}\circ R = \{(1,5), (1,4), (2,4), (3,4), (3,6)\}$\\
%%%
%d.
%%% 
}

\end{problem}