Propositional Logic; Im lost!

Question

The proof I have to solve is:

$$\lnot Z,~ \bigg((\lnot Z \lor S) \lor T\bigg) \implies L \vdash L \lor T$$

Basically I have tried to work backwards trying to prove the contradiction of $L \lor T$ but cannot seem to find how to connect these two parts, am I doing to much work or something wrong??

What proof system are you using ? – Mauro ALLEGRANZA Mar 21 '16 at 19:52 — Mauro ALLEGRANZA, Mar 21 '16 at 19:52

score 1 · Answer 1 · answered Mar 22 '16 at 06:50

1

Since you know $\neg Z$ we may use $\vee-$introduction to show $(\neg Z\vee S)\vee T$. Thus using modus ponens ($\rightarrow-$elimination) we may conclude $L$. Now use $\vee-$introduction on $L$ to conclude $L\vee T$, and we are done.

answered Mar 22 '16 at 06:50

Ove Ahlman

4,329

Propositional Logic; Im lost!

1 Answers1