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

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

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

Given information:

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

Proof:

Let us assume that R and S are reflexive and let a∈A.

By the definition of reflexive and using that R is reflexive:

(a,a)∈R

By the definition of reflexive and using that S is reflexive:

(a,a)∈S

By the definition of the union, using that (a,a