In 37-42, assume that R and S are relations on a set A. Prove or disprove each statement.

If R and S are symmetric, is R ∪ S symmetric? Why?

To prove or disprove that if R and S are symmetric, then R∪S is symmetric.

Given information:

Assume that R and S are relations on a set A and both are symmetric.

Proof:

Let us assume that R and S are symmetric and let (a,b)∈R∪S.

By the definition of the union and using (a,b)∈R∪S:

(a,b)∈R or (a,b)∈S

By the definition of symmetric: