Question

Suppose R is a symmetric and transitive relation on a set A, and there is an element a in A for which aRx for every x in A. Prove that R is reflexive.

Answer 1

let \[b\in A\]

then \[aRb\]

and by symmetry \[bRa\]

and by transitivity \[bRa,aRb\Rightarrow bRb\]

Answer 2

awesome. thanks!