- #1
vikkisut88
- 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.
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