Use an ordinary proof (not conditional or indirect proof):
1.K ∨ (S • N)
2.∼(K • ∼Q)
3.∼(N • ∼Q)
/ Q

Question

Quizplus · Accepted Answer

The Answer is To prove Q using an ordinary proof with the given premises, we will proceed step by step, applying logical rules to derive the conclusion. Here are the premises:

1. K ∨ (S • N) (Premise)
2. ∼(K • ∼Q) (Premise)
3. ∼(N • ∼Q) (Premise)

We want to prove: Q

Let's start the proof:

4. ∼K ∨ Q (De Morgan's Law on premise 2)
5. ∼N ∨ Q (De Morgan's Law on premise 3)
6. (K ∨ S) • (K ∨ N) (Distribution on premise 1)
7. K ∨ S (Simplification on step 6)
8. K ∨ N (Simplification on step 6)
9. ∼K ∨ ∼K ∨ Q (Addition on step 4)
10. ∼K ∨ Q (Tautology on step 9)
11. Q ∨ Q (Resolution on steps 8 and 10)
12. Q (Tautology on step 11)

Therefore, Q is proven using the premises provided.

Use an Ordinary Proof (Not Conditional or Indirect Proof)