Problem 2. (25 points) We wish to investigate a new property of relations which we will call Lottian. A relation R on a set A is Lottian if: Va, b, c € A: bRa A cRa → bRe a) Below is a supposed proof that any Lottian relation is reflexive. Explain any and all issues with the proof: 'Let R be a Lottian relation on the set A. Let z be an arbitrary element of A. We need to show that Rr. Let y be any element in A such that Ry. Then we know that RyATRy is true. Thus since R is Lottian, R is also true as desired.' b) Construct an example of a relation that is Lottian but not reflexive. c) Prove that if a relation R is reflexive and Lottian then R is an equivalence relation.