Prove the following parts of Theorem 2.2.1: For all sets A , B and C A ⊆ A ∪ B

Write down four distinct elements of the set {z ∈ C : z − z ̄ = 2i}.

For a fixed set A. Which of the following propositions expresses the fact that the intersection of any two subsets of A is in A? O (VX = P(A)) (VY = P(A))(3Z = P(A)) (Va € A)(a € Z ⇒ (a € XV\a € Y)) O (VX = P(A)) (VY = P(A))(=Z = P(A)) (Va € A) ((a ≤ X ^ a € Y) = a € Z) O (VX € P(A))(VY = P(A))(=Z = P(A)) (Va € A)((a ≤ XV a € Y) ⇒ a € Z) O (EZ = P(A)) (VX = P(A))(VY = P(A)) (Va € A) (a € Z ⇒ (a € X ⇒ a € Y))

6

Disprove the following statement.

Prove that if A, B, and C are sets, then (A − (C U B)) U (A N (C u Bº) °) = An Cº