Suppose that a, b, m, and n are integers (n, m positive) and suppose we know a = b (mod n) and n | m Can we safely conclude that a = b (mod m)? (a) True by transitivity (b) False because I can find small integers for which it fails. True, because congruence mod n has more equivalence classes so the conclusion is just a weaker (c) version of the hypothesis. True, because congruence mod n has fewer equivalence classes so the conclusion is just a weaker O (d) version of the hypothesis.

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