IfRandSare both reflexive, thenR∩Sis reflexive, too. I need to prove this with relational algebra or disprove by giving a counterexample. Any help? (Rock)

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- Mar 10th 2009, 12:17 AMthehollow89Prove 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? (Rock) - Mar 10th 2009, 02:51 AMPlato
- Mar 10th 2009, 08:04 AMthehollow89
- Mar 10th 2009, 08:37 AMPlato
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. - Mar 10th 2009, 11:13 AMthehollow89