Question

How do i prove this?

Answer 1

Let's consider reflexivity. We want to know if x R x. By definition, this is true if and only if x R1 x and x R2 x. Can you determine if either/both of those are true? Keep in mind that R1 and R2 themselves are equivalence relations.

Answer 2

This is an exercise in working through definitions. One needs to check that x R x and x R y implies y R x. Using the fact that R1 and R2 are both equivalence relations themselves (and thus individually reflexive and symmetric) you can verify that the two aforementioned properties hold with 1-2 logical steps.