Let A, B, and C be sets. Show that

a) (A ∪ B) ⊆ (A ∪ B ∪ C).

b) (A ∩ B ∩ C) ⊆ (A ∩ B).

c) (A − B) − C ⊆ A − C.

d) (A − C) ∩ (C − B) = ∅.

e) (B − A) ∪ (C − A) = (B ∪ C) − A.

Let A, B, and C be sets. Show that

a) (A ∪ B) ⊆ (A ∪ B ∪ C).

b) (A ∩ B ∩ C) ⊆ (A ∩ B).

c) (A − B) − C ⊆ A − C.

d) (A − C) ∩ (C − B) = ∅.

e) (B − A) ∪ (C − A) = (B ∪ C) − A.