5 Lined Rules of Inference Question

Question

Use the rules of inference together with basic logical equivalences to show that the following argument is valid. Name the rule you use at each step.

w ∨ ¬z → r

s ∨ ¬w

¬t

z → t

¬z ∧ r → ¬s

—————–

∴ ¬w

I'm really not sure how to work through this problem, I've never worked on a 5 line inference question so I'm not sure how to grasp this.

Answer 1

Hint

With $\lnot t$ and $z \to t$ derive $\lnot z$ [with Modus tollens].

With $\lnot z$ and $w ∨ ¬z → r$ derive $r$ [with Addition and Modus ponens].

With $r$ and $\lnot z$ and $¬z ∧ r → ¬s$ derive $\lnot s$ [with Conjunction and Modus ponens].

With $\lnot s$ and $s ∨ ¬w$ derive $¬w$ [with Disjunctive syllogism].