WTW 115 Tutorial 7: Unit 3.2
1. In this question, Logical Equivalence Laws and Inference Rules do not
need to be named.
Let A, B, and C be subsets of a universal set U . Use the element
method to prove the following.
(a) (A ∩ B) ∪ (A − B) ⊆ A.
(b) A × B ⊆ (A ∪ C) × B.
(c) A − (A − B) = A ∩ B.
(d) A ∪ (B − A) = A ∪ B.
(e) (A ∩ B) ∩ (A − B) = ∅.
(f) If A ⊆ B, then A ∩ (B c ∪ Ac ) = ∅.
2. Let A, B, and C be subsets of a universal set U . Use set identities
to prove the following. Using the same identity multiple times in one
step is OK, but do not combine two or more different identities in one
step.
(a) (A − B) ∪ (C − B) = (A ∪ C) − B.
(b) (B c ∪ (B c − A))c = B.
(c) (A ∪ B) ∩ (C ∩ Ac )c = A ∪ (B ∩ C c ).
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