The following is a proof that for all sets A and B, if A ?
Chapter 6, Problem 4E(choose chapter or problem)
Problem 4E
The following is a proof that for all sets A and B, if A ⊆ B, then A ∪ B ⊆ B. Fill in the blanks.
Proof: Suppose A and B are any sets and A ⊆ B. [We must show that (a).] Let x ∈ (b). [We must show that (c).] By definition of union, x ∈ (d) (e) x ∈ (f). In case x∈ (g), then since A ⊆ B, x∈ (h). In case x ∈ B, then clearly x ∈ B. So in either case, x ∈ (i) [as was to be shown].
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