Let S = {a, b, c, d, e} and define f : S → (S) by f(a) = {a, e}, f(b) = {a, c, d}, f(c) = {b, d}, f(d) = v, and f(e) = {c, d, e} .
(a) Find the set T = {x ∈ S : x ∉ f(x)} .
(b) Note that T ∉ rng f. Is it possible to find some function g : S → (S) such that T ∈ mg g, where T = {x ∈ S : x ∉ g(x)}?
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