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What is the dual of the statement (p ∧ q) ∨ ∼ q = p ∨ ∼ q?

1. (p ∨ q) ∨ ∼ q = p ∨ ∼ q
2. (p ∧ q) ∧ ∼ q = p ∧ ∼ q
3. (p ∧ q) ∨ ∼ q = p ∨ ∼ q
4. (p ∨ q) ∧ ∼ q = p ∧ ∼ q

Correct answer: (p ∨ q) ∧ ∼ q = p ∧ ∼ q

Solution

The dual is obtained by interchanging AND and OR (and T,F). (p AND q) OR ~q = p OR ~q becomes (p OR q) AND ~q = p AND ~q.

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