Below is a group of 4 arrow diagrams. F A B C D E 1 2 3 4 5 G A B C D E 1 2 3 4 5 H A B C D E 1 2 3 4 5 J A B C D E 1 2 3 4 5 Select all of the following statements that are true: F is a function. G is a function. H is a function. J is a funciton. F is right-unique. G is left-unique. H is surjective. J is a bijection. None of the above.
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Step 1: A function is a relation where each input has exactly one output. Show more…
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Problem 2: Let f: A → B and g: B → C be functions. Disprove the following statements: (1) If g ∘ f is injective, then both f and g are injective. (2) If g ∘ f is surjective, then both f and g are surjective. (3) If g ∘ f is bijective, then both f and g are bijective. Remark/Hint: To help you find counterexamples for the above (false) statements, here are three statements that are true (this is not part of the HW, just hopefully some help): (1*) If g ∘ f is injective, then f is injective. (2*) If g ∘ f is surjective, then g is surjective. (3*) If g ∘ f is bijective, then f is injective and g is surjective.
Sri K.
Consider the following function f. f('g')= 6 f('h')= 1 f('i')= 8 f('j')= 4 f('k')= 5 f('l')= 8 f('m')= 6 f('n')= 4 Recognizing that this function has a domain of {'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n'} and a codomain of {1, 4, 5, 6, 8}, which of the following is true? Select one: a. f is injective, but not surjective b. f is bijective c. None of the above d. f is surjective, but not injective
Adi S.
Say whether the following function is injective, surjective, bijective, or none of the above (note: you can only select one option): Domain: A = {1, 2, 3, 4, 5, 6} Codomain: B = {w, x, y, z} f = {(3, w), (4, z), (1, z), (6, w), (5, x), (2, x)}
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