Prove that the relation ≈ of being isomorphic, described in Definition 3. 7, is an equivalence relation on any set of binary structures. You may simply quote the results you were asked to prove in the preceding two exercises at appropriate places in your proof.

Data from Definition 3.7

Definition : Let (S, *) and (S', *') be binary algebraic structures. An isomorphism of S with S' is a one-to-one function ∅ mapping S onto S' such that  ∅(x * y) = ∅(y) *' ∅(y) for all x, y ∈ S. homomorphism property