Question: 1. (a) Let A be a set. Let X = {{o} |a e A}. Prove that X is a partition of A. What equivalence relation

1. (a) Let A be a set. Let X = {{o} |a e A}. Prove that X is a partition of A. What equivalence relation has X as its set of equivalence classes? (b) If f : A - B is onto (f[A] = B), and X is a partition of B. Let Y = {f-1[x] | re X}. Prove that Y is a partition of A. Why did you need to assume that f is onto (or did you really need to assume that?)

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