Question

Show that s is a valid conclusion from the premises. p → q, p → r, ¬(q ∧ r), s ∨ p​ ?

Answer 1

To show that s is a valid conclusion, we can use the process of modus tollens to analyze the given premises and their logical implications.

Step-by-step explanation:

To prove that s is a valid conclusion from the given premises, we can use the process of modus tollens. Let's break down each premise and step through the logic:

1. p → q: This premise states that if p is true, then q must also be true.
2. p → r: This premise states that if p is true, then r must also be true.
3. ¬(q ∧ r): This premise states that q ∧ r (both q and r being true) is false, or in other words, at least one of them must be false.
4. s ∨ p: This premise states that either s or p (or both) is true.

Now, let's use modus tollens:

1. From premise 1 and 2, if p is true, then both q and r must be true.
2. This contradicts premise 3, which states that q ∧ r is false.
3. Therefore, p cannot be true in this case.
4. Since s ∨ p is true, s must be true.

Therefore, s is indeed a valid conclusion from the given premises.

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