0

Let p, q, r, s and t be statements variables. Use the valid argument forms to deduce the conclusion, ¬q, from the premises, giving a reason for each step.

(a) ¬p ∨ q → r.

(b) s ∨ ¬q

(c) ¬t

(d) p → t

(e) ¬p∧r → ¬s

——————————————————

(f) ∴ ¬q

I have tried modus pollen on (c) and (d) but I can't find anyway to link to the other premise.

I have also tried double negation law and de morgan's law on (e), followed by hypothesis syllogism resulting in p∨¬r → ¬q but it also got me to nowhere.

Ronald
  • 21

1 Answers1

1

You are on the right track. You get $\neg p$ from modus tollens on (d). Now (a) gives you $r$. Now that you have $\neg p$ and $r$ statement (e) gives $\neg s$. (b) now forces $\neg q$.

Randall
  • 18,542
  • 2
  • 24
  • 47
  • I am sorry, what do you mean by (a) gives r, do you mean I can use ¬ from (c) and (d). Which rule did you use? – Ronald Dec 29 '20 at 03:28
  • Since $\neg p$ is true, so is $\neg p \vee q$: that's just the truth-definition of $\vee$. Likewise, since $\neg p \vee q$ is true, so is $r$: that's just the truth table for $\rightarrow$. Etc. – Randall Dec 29 '20 at 03:34
  • 1
    oh now I get what you meant, thank you so much I didn't know you could see it like that when answering rules of inference qn – Ronald Dec 29 '20 at 03:46