Let f, f1, f2: X → Y and g, g1, g2: Y → Z be functions, in which X, Y and Z are (non-empty) sets.

(1) Prove that if g is 1–1 (i.e., injective) and g ◦ f1 = g ◦ f2, then f1 = f2.

(2) Disprove the statement: If g1 ◦ f = g2 ◦ f then g1 = g2.

Answer rating: 100% (QA)

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