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What is the inverse of the proposition (p ∧ ∼ q) → r?

1. ∼(p ∨ ∼ q) → ∼ r
2. (p ∨ ∼ r) → ∼ r
3. (∼ p ∨ q) → ∼ r
4. None of these

Correct answer: (∼ p ∨ q) → ∼ r

Solution

The inverse of p->q is (~p)->(~q). Here antecedent is (p ^ ~q) and consequent is r, so the inverse is ~(p ^ ~q) -> ~r = (~p v q) -> ~r.

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