I have this equivalence relation problem:
Let $R$ and $S$ be two equivalence relations on the same set $A$. Define a new relation $U$ such that $U(x,y) \leftrightarrow [R(x,y) \text{ or } S(x,y)]$. Is $U$ necessarily an equivalence relation?
I said that is was an equivalence relation because $U$ is only true if $R$ or $S$ is true, and only depends on one. I do not know know exactly how to explain it, or prove this. Should I use proof by contradiction to prove this and make the negated statement $!U(x,y) \leftrightarrow {![R(x,y) \text{ or } S(x,y)]}$ and from this we can see that $U$ is an equivalence relation because the negation is saying that $R(x,y)$ or $S(x,y)$ isn't an equivalence when it actually is?
I am kind of stuck so any help is appreciated.