1. A relation R on a set A is called circular if for all a, b ∈ A, a R b and b R c imply c R a. Prove: A relation is an equivalence relation iff it is reflexive and circular
2. (a) Define an ordered triple (a, b, c) to be equal to ((a, b), c). Prove that (a, b, c) = (d, e, f ) iff a = d, b = e, and c = f.
(b) On the basis of our definition of an ordered pair (a, b) as {{a}, {a, b}}, we might be tempted to define an ordered triple (a, b, c) as {{a}, {a, b}, {a, b, c}}. Show by means of an example that this will not work. That is, find two different ordered triples that have equivalent representations in this set notation