Thread: Prove with relational algebra

If R and S are both reflexive, then R ∩ S is reflexive, too. I need to prove this with relational algebra or disprove by giving a counterexample. Any help?

Originally Posted by thehollow89

If R and S are both reflexive, then R ∩ S is reflexive, too. I need to prove this with relational algebra or disprove by giving a counterexample.

Any reflexive relation on a set contains the diagonal of the cross product of the set with itself. So does it follow that the intersection of two reflective relations must be reflexive?

Originally Posted by Plato

Any reflexive relation on a set contains the diagonal of the cross product of the set with itself. So does it follow that the intersection of two reflective relations must be reflexive?

Oh I know it's reflexive, but how exactly am I supposed to show that?

Originally Posted by thehollow89

Oh I know it's reflexive, but how exactly am I supposed to show that?

Suppose that each of is a reflexive relation on .
That means .
That is the whole proof that is reflexive.

Originally Posted by Plato

Suppose that each of is a reflexive relation on .
That means .
That is the whole proof that is reflexive.

Oh thanks. I really do assume that proofs are harder than they actually are.