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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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    http://www.proofwiki.org/wiki/Intersection_of_Reflexive_Relations_is_Reflexive2011-10-07

2 Answers 2

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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.

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Use proof by contradiction. Suppose that $R\cap S$ is not reflexive. Use definition of intersection to show a contradiction.