Relations can be composed just as functions are composed (for instance $\displaystyle g~ o~ f$).. note that the "o" is meant to be the "of" symbol but didn't know how to do it in latex.

For each of the following below, either prove or provide a counterexample:

a.) If $\displaystyle R$ is reflexive and if $\displaystyle S$ is reflexive, then $\displaystyle S~o~R$ is reflexive.

b.) If $\displaystyle R$ is symmetric and $\displaystyle S$ is symmetric, then $\displaystyle S~o~R$ is symmetric.

c.) If $\displaystyle R$ is transitive and $\displaystyle S$ is transitive, then $\displaystyle S~o~R$ is transitive.