Let A and B be any sets. Prove: (a) A is the disjoint union of AB and A ∩ B. (b) A ∪ B is the disjoint union of AB, A ∩ B, and BA.
Added by Jeffrey S.
Step 1
This means that we need to show two things: (1) A = AB ∪ (A ∩ B) and (2) AB ∩ (A ∩ B) = ∅. (1) To show that A = AB ∪ (A ∩ B), we need to show that every element in A is either in AB or in A ∩ B, and that every element in AB ∪ (A ∩ B) is in A. Let x ∈ A. If x ∈ Show more…
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