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.

According to what I have researched, here is how you prove that R is reflexive.
let b∈A
then, aRb
and by symmetry, bRa
and by transitivity,bRa,aRb⇒bRb
Hope this is the answer that you are looking for. 
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