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Answer: A symmetric relation R on S is that For all $x,y\in S$ such that $xRy$ implies $yRx$. meaning if the element x is related to y, then it is also true the other way around that element y is related to x of the set S.

i.e. $xRy\rightarrow yRx$

Does my definition wordings correct?

Surdz
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  • correct, but better use $\forall$ symbol: $\forall x,y\in S(xRy\rightarrow yRx)$ – boaz May 28 '16 at 22:08
  • can I get a basic home work question of the above relation to solve? – Surdz May 28 '16 at 22:11
  • A nice HW practice question: prove that if $R$ is a non empty symmetric and transitive relation over $S$, then it must be reflexive. – boaz May 28 '16 at 22:19

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