I have this problem for my Assignment due tomorrow that I'm very stuck on. I need to prove the validity if the conclusion. Please help me! Thanks!
w $\lor$ $\lnot$z $\to$ r
s $\lor$ $\lnot$w
$\lnot$t
z $\to$ t
$\lnot$z $\land$ r $\to$ $\lnot$s
conclusion: $\lnot$w
From statements $3$ and $4$ and Modus Tollens we have $\lnot z$.
From $\lnot z$ and Addition, we get $w \lor \lnot z$, which by Modus Ponens in statement 1 implies $r$.
Then by Conjunction on $r$ and $\lnot z$, we have $\lnot z \land r$, which with Modus Ponens on statement $5$ gives $\lnot s$.
Then using Disjunctive Syllogism on statement $2$ and $\lnot s$, we have $\lnot w$.
If you have questions on the specific rules used, see https://en.wikipedia.org/wiki/Propositional_calculus#Basic_and_derived_argument_forms, there is a big table partway down with all of them.