College level, not hard but need specific steps.#1. The dist
College level, not hard but need specific steps.#1. The distinction between ⊆ and ∈. Recall that for sets A and B, A ⊆ B meansthat A is a subset of B. Recall also that x ∈ C means that x is an element of C. Also,y /∈ D means that y is not an element of D. Let ∅ denote the empty set.(1a) We have already proved that ∅ ⊆ A for any set A. However, ∅ ∈ ∅ / ; explain why. (1b) Explain why ∅ ∈ P(X) for any set X, where P(X) is the power set of X. (1c) Let U be the universal set. Suppose that A and B are sets. Explain why A − B ∈P(A), where A − B is the set difference of A and B.(1d) It is possible for x, A, and B to be such that x ∈ A and A ∈ B. Given an example.(1e) It is possible that both A ∈ B and A ⊆ B. Given an example.
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