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lockedup
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Homework Statement
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.
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.