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)}

Exercise

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

This is not the right answer. Remember: two elements are in a relation if their set-theoretical notation depicts them within round brackets. In an asymmetric relation, if an element a, for example, is in the relation R with b, then b CANNOT be in the same relation with a. For example, R = {(a,b), (c,d), (b,a), (c,b)} is NOT an asymmetric relation.

This is not the right answer. Remember: two elements are in a relation if their set-theoretical notation depicts them within round brackets. In an asymmetric relation, if an element a, for example, is in the relation R with b, then b CANNOT be in the same relation with a. For example, R = {(a,b), (c,d), (b,a), (c,b)} is NOT an asymmetric relation.

This is not the right answer. Remember: two elements are in a relation if their set-theoretical notation depicts them within round brackets. In an asymmetric relation, if an element a, for example, is in the relation R with b, then b CANNOT be in the same relation with a. For example, R = {(a,b), (c,d), (b,a), (c,b)} is NOT an asymmetric relation.

Good job, you got it right! You're already on your way to becoming a mathematical psychologist!