Is symmetry biconditional?

No.11602048 ViewReplyOriginalReport
As in if (x,y) is an element of R, then (y,x) is an element of R.
Is it true then, that if (y,x) is element of R, then (x,y) is also an element of R?

Also, what if (x,y) is NOT an element of R, what can we say about (y,x)?