[24 points] We wish to investigate a new type of relation which we will call Vahidean. A relation R on the set A is Vahidean if: ∀a, b, c ∈ A aRb ∧ aRc → bRc a) Explain, in English, how Transitivity and Vahideanness are different. Give an example of a Vahidean relation on {a, b, c, d} which is not transitive (draw its digraph representation). Give a counterexample that shows your relation is not transitive. b) Is the following an implication of Vahideanness? ∀a, b, c ∈ A aRb ∧ aRc → cRb Explain why or why not. c) Prove that if a relation R is Reflexive and Vahidean then R is an equivalence relation.