# Given reflexive relations $R$ and $S$ on $X$, $R\cap S$ is reflexive

Give a proof or counterexample.

Given reflexive relations $R$ and $S$ on $X$, $R\cap S$ is reflexive.

This would be true, correct?

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Please make the body of your post self-contained, instead of relying on the subject for key content. –  Arturo Magidin Oct 6 '11 at 19:42
Well, do you have a proof, or do you have a counterexample? –  Arturo Magidin Oct 6 '11 at 19:43
proofwiki.org/wiki/… –  Martin Sleziak Oct 7 '11 at 10:24

If $R$ and $S$ are reflexive relations on a set $X$, then $(x,x)\in R$ and $(x,x)\in S$ for all $x\in X$, so $R\cap S$ is reflexive as well.
Use proof by contradiction. Suppose that $R\cap S$ is not reflexive. Use definition of intersection to show a contradiction.