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I am having difficulties understanding how do I perform set operation like union or intersection on Relations.

In a question, I am asked to prove/disprove:

  • If R & S are symmetric, is $R \cap S$ symmetric?
  • If R & S are transitive, is $R \cup S$ transitive?

How do I do that? 1st, how does $R \cap S$ or $R \cup S$ look like? How can I write a formal prove/disprove for it? I am very bad at these proves ...

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    See [Intersection of Symmetric Relations is Symmetric](http://www.proofwiki.org/wiki/Intersection_of_Symmetric_Relations_is_Symmetric) at ProofWiki.2012-09-18
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    Remember that (in the usual set-based formalism) a relation $R$ is simply a set of ordered pairs: $R=\{(x,y)\mid x\mathrel{R} y\}$ by definition. So $R\cap S$ is the realation such that $x\mathrel{(R{\cap}S)} y$ iff $x\mathrel{R}y \land x\mathrel{S}y$.2012-09-18

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