Consider the two sets A = {n EN:n is both a perfect square and a perfect cube} and B = {r € N:r = 0mod 7 or r = 1mod 7). If one

Question

Consider the two sets A = {n EN:n is both a perfect square and a perfect cube}
and B = {r € N:r = 0mod 7 or r = 1mod 7). If one wishes to prove A = B. then which of the
following describes a valid proof strategy? Select only one answer.
(a) Suppose z € A and prove r e B, and then suppose r&A and show r & B.
(b) Suppose z E A and prove z € B.
(c) Suppose z € An B and conclude re AUB.
(d) Suppose z € B and conclude z E A. and then suppose z E A and conclude a contradiction.
(e) Suppose z B and conclude z € A.

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