In, construct an algebraic proof for the given
Chapter 6, Problem 34E(choose chapter or problem)
Problem 34E
In, construct an algebraic proof for the given statement. Cite a property from Theorem for every step.
Cite a property from Theorem
Deriving a Set Difference Property
Construct an algebraic proof that for all sets A, B, and C,
(A ∪ B) – C = (A – C) ∪ (B – C).
Cite a property from Theorem 6.2.2 for every step of the proof.
Solution Let A, B, and C be any sets. Then
Exercise
For all sets A, B, and C,
(A – B) – C = A – (B ∪ C).
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