I just started my abstract algebra class and I am struggling with the concept of equivalence relations. I know that in order to prove equivalence relations, I have to prove the reflexive, symmetric, and transitive properties. However, I don't know how to go about starting the actual proof or solution. I have these examples and any help would be appreciated.
a) Given sets $A$ and $B$, explain why $A~B$ is equivalent to asserting $B \sim A$
b) For three sets $A, B$, and $C$, show that $A \sim B$ and $B \sim C → A \sim C$
Thank you for any help!