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

A relation R is said to be symmetric iff for any pair a and b if a is in the relation R with b, then also b is in the relation R with a.

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

Practical tip: You can spot a symmetric relation in its set-theoretical notation by checking if each couple of elements are repeated, but in a reverse order.

The following symmetric relation:

aRb, bRa

Can be represented in a set-theorical notation:

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

Exercise

Take a look at sets bellow. Which of the four below is a symmetric relation?

Darn, you almost got it, but this is not the right answer. Remember: two elements are in relation if their set-theoretical notation depicts them within round brackets. In a symmetric relation, if an element a is in relation with b, then also b is in the same relation with a (i.e., R = {(a, b), (b, a)}).”

Darn, you almost got it, but this is not the right answer. Remember: two elements are in relation if their set-theoretical notation depicts them within round brackets. In a symmetric relation, if an element a is in relation with b, then also b is in the same relation with a (i.e., R = {(a, b), (b, a)}).”

Darn, you almost got it, but this is not the right answer. Remember: two elements are in relation if their set-theoretical notation depicts them within round brackets. In a symmetric relation, if an element a is in relation with b, then also b is in the same relation with a (i.e., R = {(a, b), (b, a)}).”

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