Exercise give certain properties of functions that we shall encounter later in the text. You are to do two things:
(a) rewrite the defining conrutions in logical symbolism using ∃, ∋, and ⇒ , as appropriate; and
(b) write the negation of part (a) using the same symbolism. It is not necessary that you understand precisely what each term means. Ex ample: A function f is odd if for every x, f(–x) = –f(x). (a) defining condition: ∀x, f(–x) = –f(x). (b) negation: ∃ x ∋ f(-x) ≠– f(x).
A function.f: A → B is injective if for every x and y in A, if f(x) = f(y), then x = y.
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