Using transitive to prove symmetric

Question

Consider a relation R on a set A. Prove R is symmetric if R is transitive and there exists a c in A such that for every x in A, xRc and cRx. Help!!

Take $x$ and $y$ in $A$. Then if $x$~$y$ then $y$~$c$ and $c$~$x$ then by transitivity; $y$~$x$ — SEWillB, May 04 '17 at 15:06

Meneer-Beer · Answer 1 · 2017-05-04T15:59:11.040

0

Assume $x,y\in A$ and $xRy$. We must show that $yRx$. We know that $xRc$ and $cRy$, by assumption. Since R is transitive we have $xRc \land cRy \rightarrow yRx$, proving that R is symmetric.

edited May 04 '17 at 15:59

answered May 04 '17 at 15:21

Meneer-Beer

324

@Arthur I had. It is corrected now. – Meneer-Beer May 04 '17 at 15:54

Using transitive to prove symmetric

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