Prove or disprove: Let 1 and 2 be relations on a set .
a) If 1 and 2 are reflexive relations, then 1 ∪ 2 is reflexive.
b) If 1 and 2 are symmetric relations, then 1 ∪ 2 is symmetric.
c) If 1 and 2 are transitive relations, then 1 ∪ 2 is transitive.
So my confusion stems from the fact that, doesn't R1 U R2 mean R1 or R2? So if they are both reflexive and then it says to prove if one or the other is reflexive then isn't it a given?
Could someone also maybe help solve one part to guide me on solving the rest? Thanks