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!!

Answer 1

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.