Stuck on a deductive proof

Question

Premises    (p → t) ∨ q
             r → s
            (p ∨ q) → r
 Conclusion s

Very new to deductive proofs, I have the 3 above premises and a conclusion. I am confused as to why the answer is not just one line stating that (p ∨ q) → ris equal to s using `r → s, believe the rule is called the law of equivalence

The conclusion does not follow from the premises. – Mauro ALLEGRANZA Apr 03 '17 at 20:49 — Mauro ALLEGRANZA, Apr 03 '17 at 20:49
What do you mean? As in my premises are incorrect? – Peter Wilson Apr 03 '17 at 20:50 — Peter Wilson, Apr 03 '17 at 20:50

score 0 · Accepted Answer · answered Apr 03 '17 at 20:53

0

HINT

Notice in your premises, the only way to conclude $s$ is to prove that $r$ is true, and that is only possible if $p \vee q$ is true. Is it possible to derive this from your first statement?

answered Apr 03 '17 at 20:53

gt6989b

54,422

I had a feeling the first premise was incorrect, if is was (t → p) ∨ q then I would be able to conclude s, correct? – Peter Wilson Apr 03 '17 at 20:57
@PeterWilson yes, you are right – gt6989b Apr 03 '17 at 21:01
I have completed it there, thank you very much! – Peter Wilson Apr 03 '17 at 21:02

Stuck on a deductive proof

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