This is intro to abstract mathematics Part 1 Let f(x) = x 2 . Determine the following sets (no proof needed): f({1,-1}), f 1 ((0,1)), f( f 1 ({ -1})),...

This is intro to abstract mathematics

Part 1

Let f(x) = x2. Determine the following sets (no proof needed): f({1,-1}), f −1((0,1)), f( f −1({ -1})), and f-1(f({1}))

Part 2

Let f: X → Y be a function and A⊂X. By definition it is always true that if x∈A then f(x) ∈ f(A). Prove or disprove: If x∉A then f(x) ∉ f(A).

Part 3

For any function f, prove that f(Ø) = Ø and f −1(Ø) = Ø