Give a proof or counterexample.
Given reflexive relations $R$ and $S$ on $X$, $R\cap S$ is reflexive.
This would be true, correct?
Give a proof or counterexample.
Given reflexive relations $R$ and $S$ on $X$, $R\cap S$ is reflexive.
This would be true, correct?
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.