1. Suppose that A ⊆ B ⊆ C and A ~ C. Prove that A ~ B and B ~ C. 2. Determine whether each of the following is True or False. Explain your answers. (a) For every set S, ∅ ⊆ p (S). (b) For every set S,...

1. Suppose that A ⊆ B ⊆ C and A ~ C. Prove that A ~ B and B ~ C.

2. Determine whether each of the following is True or False. Explain your answers.

(a) For every set S, ∅ ⊆ p (S).

(b) For every set S, ∅ ∈ p (S).

(c) {2} ⊆ p ({2, 3}).

(d) {2} ∈ p ({2, 3}).

(e) {{2}} ⊆ p ({2, 3}).