Let f: A → B be a function and let A₁, A₂ ≤ A and B₁, B₂ ≤ B. (a) Prove that f-¹[B₁ UB₂] = ƒ¯¹[B₁] Uƒ˜¹[B₂]. (b) Prove that f[A₁ UA₂] = ƒ[A₁] Uƒ[A₂]. (c) Prove that f-¹[B₁ \ B₂] = f¯¹[B₁] \ ƒ¯¹[B₂]. (d) Provide an example such that f[A1 \A2] # ƒ[A1]\ ƒ[A₂]. Provide a condition on f that implies that ƒ[A₁ \ A₂] = ƒ[A₁]\ƒ[A₂].

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