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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.