6. (i) Prove or can give a counterexample for each of the following claims:
a.) A ∪ B ⊆ A ∩ B.
b.) A ∩ B ⊆ A ∪ B
(ii) Prove that (A ∪ B) \ (A ∩ B) = (A \ B) ∪ (B \ A).
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Step-by-step explanation:
(A ∪ B) \ (A ∩ B) = (A \ B) ∪ (B \ A)
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A ∪ B ⊆ A ∩ B.
A ∩ B ⊆ A ∪ B
(A ∪ B) \ (A ∩ B) = (A \ B) ∪ (B \ A).
Hence proved.
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