- #1

- 34

- 0

Let f: X → Y and A is a subset of Y and B is a subset of Y. Prove that:

a) f⁻¹(A union B) = f⁻¹(A) union f⁻¹(B)

b) f⁻¹(A intersetion B) = f⁻¹(A) intersection f⁻¹(B).

I know that f⁻¹(A) = {x ε X : f(x) ε A}

and so f⁻¹(B) {x ε X : f(x) ε B}

but after that I really don't understand how to prove this.

a) f⁻¹(A union B) = f⁻¹(A) union f⁻¹(B)

b) f⁻¹(A intersetion B) = f⁻¹(A) intersection f⁻¹(B).

I know that f⁻¹(A) = {x ε X : f(x) ε A}

and so f⁻¹(B) {x ε X : f(x) ε B}

but after that I really don't understand how to prove this.

Last edited: