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?
Suppose that each of $\displaystyle R\;\&\;S$ is a reflexive relation on $\displaystyle A$.
That means $\displaystyle \Delta _A \subseteq R\;\& \;\Delta _A \subseteq S\; \Rightarrow \;\Delta _A \subseteq R \cap S$.
That is the whole proof that $\displaystyle R \cap S$ is reflexive.