# Thread: Prove with relational algebra

1. ## Prove with relational algebra

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

2. Originally Posted by thehollow89
If R and S are both reflexive, then RS 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?

3. 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?

4. Originally Posted by thehollow89
Oh I know it's reflexive, but how exactly am I supposed to show that?
Suppose that each of $R\;\&\;S$ is a reflexive relation on $A$.
That means $\Delta _A \subseteq R\;\& \;\Delta _A \subseteq S\; \Rightarrow \;\Delta _A \subseteq R \cap S$.
That is the whole proof that $R \cap S$ is reflexive.

5. Originally Posted by Plato
Suppose that each of $R\;\&\;S$ is a reflexive relation on $A$.
That means $\Delta _A \subseteq R\;\& \;\Delta _A \subseteq S\; \Rightarrow \;\Delta _A \subseteq R \cap S$.
That is the whole proof that $R \cap S$ is reflexive.
Oh thanks. I really do assume that proofs are harder than they actually are.