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SOLVED: a) Construct an injective function from set X into its powerset P(X) and comment on whether it is surjective or not.b) Let f:X → Y be a function. Show that R = (x1,x2) ∈ X × X | f(x1) = f(x2) defines an equivalence relation on X.c) Let S be an equivalence relation on X. Show that I = [x] | x ∈ X is a partition on X.d) Consider the partition representatives of P = 0,1, 2, # on X = 0, 1, 2, #. Construct two different sets of representatives.
SOLVED: a) Construct an injective function from set X into its powerset …
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