For each of the following sets B and binary relations ~, decide whether defines an equivalence relation on B. Justify your answer in each case. (a) Relation: x y if |x – y| < 1 Set: B = R B = Mn(R), the set of n xn matrices with real entries, where n is some fixed positive integer X ~ Y if Tr(X – Y) e Z (b) Set: Relation: (Here, Tr(X) denotes the trace of a matrix X € Mn (R).)

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Q: 40

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