(a) Define an ordered triple (a, b, c) to be equal to ((a, b), c). Prove that (a, b, c) = (d, e, f) if 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.
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