Question: 3. (20 marks) Define a relation ~ on N whereby a ~ b if and only if there exists k E Z such that 1

3. (20 marks) Define a relation ~ on N whereby a ~ b if and only if there exists k E Z such that 1 = 2k. (a) (9 marks) Prove that ~ is an equivalence relation. (b) (5 marks) Write out the equivalence classes for ~ on the set {2, 4, 6, . .., 20 }. (c) (6 marks) Prove that for all x, y E N if r ~ y and r is odd, then x

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