"The logical expression for the symmetric relation should contain the biconditional operator <-> instead of implication -> . Because, if u keep ->, then for the case when F -> T the implication still holds true which means if b,a E R is T then it means it doesn't matter if a,b E Ris T/F R will be symmetric." Could someone plz help, this seems to be correct. Also https://en.wikipedia.org/wiki/Symmetric_relation.