# Relations Question

• February 18th 2009, 02:56 AM
Halmos Rules
Relations Question
Suppose R and S are two reflexive and symmetric relations. Prove that RoS is reflexive and symmetric.

This exercise was in an exam i took a couple of days ago. I could prove that RoS is reflexive, but i couldn't prove it is symmetric ( In fact i tried to prove that RoS is symmetric iff RoS=SoR). Any help would be greatly appreciated.(Happy)
• February 18th 2009, 07:06 AM
Plato
On the set $X = \left\{ {a,b,c} \right\}$ define relations
$\begin{gathered}
S = \left\{ {(a,a),(b,b),(c,c),(a,b),(b,a)} \right\} \hfill \\
R = \left\{ {(a,a),(b,b),(c,c),(c,b),(b,c)} \right\} \hfill \\
R \circ S = \left\{ {(a,a),(b,b),(c,c),(a,b),(b,a),(a,c),(c,b),(b,c)} \right\} \hfill \\
(a,c) \in R \circ S \hfill \\
(c,a) \notin R \circ S \hfill \\
\end{gathered}$