(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm working on some set theory stuff to prepare for Topology next semester. I'm actually working out of a Topology book from Dover Publications. I could really use some direction/correction.

1. If S ⊂ T, then T - (T - S) = S.

2. If S is any set, then ∅ ⊂ S.

3. The attempt at a solution

1. Let x ∈ (S ⊂ T). Therefore, x ∉ (T – S). If x ∉ (T – S), then x ∈ T – (T – S). But x ∈ (S ⊂ T). Therefore, S ⊂ (T - (T - S))

Let x ∈ (T - (T - S)). This implies that x ∉ (T – S). Which implies that x ∈ S. Therefore, T – (T – S) ⊂ S and T - (T - S) = S.

2. A set A is a subset of a set S if every element of A is in S. If A is ∅, then A has no elements. Therefore all of its elements are in S.

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# Some Basic Set Theory Proofs

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