Hello,

I have to proof that when R and S are equivalence relations then $\displaystyle R \cup S$ is an equivalence relation if and only if $\displaystyle R \cup S=RS$.

Can anyone give me a hint?

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- Dec 9th 2012, 08:28 AMMachinePL1993Proof regarding Equivalence Relations
Hello,

I have to proof that when R and S are equivalence relations then $\displaystyle R \cup S$ is an equivalence relation if and only if $\displaystyle R \cup S=RS$.

Can anyone give me a hint? - Dec 9th 2012, 08:48 AMPlatoRe: Proof regarding Equivalence Relations
- Dec 9th 2012, 08:58 AMMachinePL1993Re: Proof regarding Equivalence Relations
Yes, $\displaystyle R,S$ are in the same domain. $\displaystyle RS$ is a composition of two relations.

- Dec 9th 2012, 09:38 AMPlatoRe: Proof regarding Equivalence Relations