Hi, Can someone take a look if I have worked through this correctly? thanks

Question 4.

~r -> p, (~p) v q, ~s -> (~p)^(~r), (~p) ^ r -> (~s) v t, ~q, therefore t.

1.~q premise

~q vp premise

therefore ~p disjunctive syllogism

2.~p from 1

~r -> p premise

therefore r modus tollens

3.~p from 1

r from 2

therefore ~p^r conjunctive addition

4.~p^r from 3

~s -> (~p)^(~r) premise

therefore s modus tollens

5.~p^r from 3

s from 4

(~p) ^ r -> (~s) v t therefore t disjunctive syllogism

thanks