Question

Use the valid argument form to deduce the conclusion from the premises, giving a reason for each step.

A. ~p v q ➵ r

B. s v ~q

C.~t

D. p ➵ t

E. ~p Λ r ➵ ~s

F. (conclusion) ~q

So Far this is my work.

p➵ t ( p implies t, if p then t, modus tolltens)
~t

conclusion ~p

~p ➵ q
(conclusion) ~p v q (generalization)

~p v q ➵ r
~ p v q

r

This is where I get stuck. Does anyone know what to do next and why?

Answer 1

Using modus tollens, modus ponens, and disjunctive syllogism, we have logically deduced ~q from the given premises coherently and validly consistent with established rules of deductive reasoning.

Step-by-step explanation:

To solve this deductive reasoning problem using the given premises to reach the conclusion ~q (not q), let's follow the logical steps. Each step should follow from the previous through a valid argument form like modus ponens, modus tollens, or disjunctive syllogism.

Step-by-Step Deduction

1. Given p → t (If p then t).
2. Given ~t (not t).
3. From 1 and 2, we can deduce ~p (not p) using modus tollens.
4. Now we have ~p, and given ~p v q → r (If not p or q then r), we can deduce r.
5. With r and given ~p ∧ r → ~s (If not p and r then not s), we deduce ~s.
6. s v ~q (s or not q) was given as a premise. With ~s now deduced, we can infer ~q using disjunctive syllogism.

Therefore, by following the valid argument forms, we have used deductive reasoning to conclude ~q, each step providing a reason establishing the coherence of our logic.