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If the implication (p → r) ⇒ (q ∨ r) is false, and both q and r are false, what can be concluded about p?

1. True
2. False
3. May be either true or false
4. The information given is sufficient

Correct answer: False

Solution

(p->r) => (q v r) is false only if (p->r) is true and (q v r) is false (q,r both false). With r false, p->r is true only when p is false. Hence p is False.

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