The following are two proofs that for all sets A and B, A
Chapter 6, Problem 2E(choose chapter or problem)
Problem 2E
The following are two proofs that for all sets A and B, A – B ⊆ A. The first is less formal, and the second is more formal. Fill in the blanks.
a. Proof: Suppose A and B are any sets. To show that A – B ⊆ A, we must show that every element in (1) is in (2). But any element in A– B is in (3) and not in (4) (by definition of A – B). In particular, such an element is in A.
b. Proof: Suppose A and B are any sets and x ∈ A – B. [We must show that (1).] By definition of set difference, x ∈ (2) and x ∉ (3). In particular, x ∈ (4) [which is what was to be shown].
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