Establishing if a binary relation expressed in set-theoretical notation is symmetric

A relation R is said to be asymmetric iff, whenever an element a is in the relation R with b, then b is not in the relation R with a:

\[R\quad is\quad asymmetric\quad \Leftrightarrow\forall a,b \in A, (aRb) \Rightarrow \neg (bRa)\]

Practical tip: You can spot an asymmetric relation in its set-theoretical notation by checking if at least one pair of elements is repeated in a reverse order. If there are no such repetitions, then the relation is asymmetric.

Consider the following relation:

aRc , bRd , aRb

On the set A = {a,b,c,d}

The relation can also be represented in a set-theorical notation:

R = {(a,c), (b,d), (a,b)}


Which of the following relations on the set A = {a, b, c, d} is actually an asymmetric relation?