"Let R and S be two relations on a set A. For each statement below, if it's true, prove it; if it's false, give a counterexample. Remember that R and S are sets of ordered pairs.

a.) If R is transitive and S is transitive, then R intersects S is transitive.

b.) If R is transitive and S is transitive, then R U (union) S is transitive.

c.) If R is transitive and S is transitive, then R - S is transitive.

I am thinking a and c are true, and b is false.

Many thanks.

Phil