Question

Call a relation R “orbital” if x R yand y R zimply z R x. Prove that R is an equivalence relation if and only R is both reflexive and orbital. (Note that this is an “if and only if” statement, which is biconditional. So there are actually two different implications to show here.)

Answer 1

first, do you know the definition of equivalence relation?
You don't have to prove that R is a relation -- they told you that.
So now use the properties of an equivalence relation.