Set Theory Proofs
Consider the following two statements. A, B, C denote arbitrary quantities. One claim is true and the other is false. Prove what is true and show that what is false is really false by producing three quantities A, B, C that meet the assumptions but not the conclusion. ( Venn diagram Proof not allowed)
i) A ⊕ C = ∅ ∧ A ∩ B ∩ C = ∅ ⇒ A ∪ C = ∅
ii) A ∩ C = ∅ ∧ B ⊂ A ∪ C ⇒ B ⊂ A ⊕ C.
bb
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