Prove that if * is an associative and commutative binary operation on a set S, then
(a * b) *(c *d) = [(d * c) * a] * b
for all a, b, c, d e S. Assume the associative law only for triples as in the definition, that is, assume only
(x * y) *z = x* (y * z)
for all x, y,z ∊ S.
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