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% " % ( % ) ) / & , 0 % 0 % 1 2 3 4 5 4 6 7 8 9 7 ;0 0 1 2 3 / 4 * $ * 5 3 & 0 1 23 4 5 6 7 8 9 5 ;3 Let A, B, C be sets, and let f A → B and g B → C be functions Prove the following statements (a) If f and g are injective, then g f is injective ProofSuppose that f and g are injective Let x;y ∈ AIf (g f)(x) = (g f)(y),then g(f(x)) = g(f(y))Since g is injective, we have f(x) = f(y)Further, since f is injective, it follows that x = yTherefore, g f is injective Composition Of Functions Discrete Mathematics Lectures ƒXƒgƒŒ[ƒg •"¯ ƒ~ƒfƒBƒAƒ€ ƒŒƒCƒ„[