Q1. Consider the sets X = {4m + 1|m ∈ Z} and Y = {2n - 1|n ∈ Z}.
(a) Prove that X ⊆ Y.
(b) Is Y ⊆ X? If yes, prove it. If not, find an element of Y that's not an element of X.
Q2. Let X be a set, and P(X) its powerset. Define a function f : P(X) → P(X) by f(A) = X\A.
(a) Consider the case X = {1, 2, 3}. Evaluate f(A) for every A ∈ P(X).
(b) For X any set, prove that f is a bijection.