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Question: i for any ab q define a b...

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(i) For any a,b є Q, define a ~ b to mean a-b є Z. Show that this defines an equivalence relation on Q. Find the equivalence class of a for any given a EQ and a complete set of representatives. Hint. Consider the problem on the real (ii) For any a, b є Z, define a ~ b to mean that a-b is an even number, i.e., that 2 divides a-b (or that a-b-2k for some k є Z). Show that this defines an equivalence relation on Z. Find the equivalence class of a for any given a Z and a complete set of representatives.

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