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Confused on proof questions about relations

Mathematics Asked by Atlecx on February 7, 2021

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

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