4. Let A and B be sets. Show thata) (A ∩ B) ⊆ A b) A ⊆ (A ∪ B) c) A − B ⊆ Ad) A ∩ (B − A) = ∅ e) A ∪ (B − A) = A ∪ B f) A ⊕ B = (A ∪ B) − (A ∩ B).

Let 𝐴 and 𝐵 be sets. Show thata) (𝐴 ∩ 𝐵) ⊆ 𝐴.b) 𝐴 ⊆ (𝐴 ∪ 𝐵).c) 𝐴 − 𝐵 ⊆ 𝐴.d) 𝐴 ∩ (𝐵 − 𝐴) = ∅.e) 𝐴 ∪ (𝐵 − 𝐴) = 𝐴 ∪ 𝐵.

Let 𝐴 and 𝐵 be sets. Using set builder notation, show that:a) 𝐴 ∩ ∅ = ∅.b) 𝐴 ∪ 𝐴 = 𝑈.c) 𝐴 ∩ (𝐵 − 𝐴) = ∅

A − (B ∪ C) = (A − B) − C.(3 marks)(b) Consider the sets S = {3, 5} and T = {2, 3, 7}. Indicate whether each of the followingstatements is true or false; no explanation is needed.(2 marks)(i) S ⊆ T(ii) ∅ ∈ P(S)(iii) ∅ ∈ T(iv) (3, 3, 3) ∈ S × T

1） Use the logical equivalences below and the definitions of set operations to prove, or provide a counterexample to disprove, the following set identity: (A ∪ B) ∖ C = (A ∖ C) ∪ (B ∖ C) 2）Use the logical equivalences below and the definitions of set operations to prove, or provide a counterexample to disprove, the following set identity: (A ∪ B) ∖ C = (A ∖ C) ∪ B

Show that the following four conditions are equivalent.(i) A ⊂ B (ii) A – B = Φ(iii) A ∪ B = B (iv) A ∩ B = A