Answer to Question #136746 in Discrete Mathematics for ashmita

Question

Let f : A → B be a function and σ an equivalence relation on B. Define a relation ρ on A as: a ρ a' if and only if f(a) σ f(a').

1. Prove that ρ is an equivalence relation on A.

2. Define a map f : A/ρ → B/σ as [a]ρ 7→ [f(a)]σ. Prove that f is injective.

3. Prove or disprove: If f is a bijection, then so is f.

4. Prove or disprove: If f is a bijection, then so is f.

Answer 1

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