A relation R on a set A is said to be symmetric if and only if
(a,b) $\in$ R
and (b,a) $\in$ R for all a,b $\in$ A
that is aRb = bRb for all a,b $\in$ A
Note: The knowledge of properties like symmetric relations is very important for the understanding of Sets. And one must not confuse one one property with the other, as each property has its unique significance.