Question

Accepting the following premises:

a.( p ∧ t ) → ( r ∨ s )
b.q → ( u ∧ t )
c.u → p
d.¬ s
Conclude that q → r.

Answer 1

To conclude that q → r, we need to make logical deductions using the given premises. By using the substitution and modus ponens rules, we can derive the conclusion q → r.

Step-by-step explanation:

In order to conclude that q → r, we need to use the given premises and make logical deductions. Let's go step-by-step:

1. From premise c (u → p) and premise d (¬ s), we can deduce that ¬ u and ¬ p are true.
2. Using premise b (q → (u ∧ t)) and the conclusion from step 1, we can substitute ¬ u for u and get q → (¬ u ∧ t).
3. From premise a ((p ∧ t) → (r ∨ s)) and the conclusion from step 2, we can substitute ¬ u ∧ t for p ∧ t and get (¬ u ∧ t) → (r ∨ s).
4. Finally, using modus ponens, we can combine the conclusions from step 3 and premise 2 to get q → (r ∨ s) as the final conclusion.

Therefore, we can conclude that q → r.