When determining the validity of this argument, you can use a truth table. But you can also use an explanation of it to a certain extent to where the validity of the argument is stated or implied.
We have p or q. And we have to assume not q and therefore get p.
1. p v q hyp
2. ~q hyp
3. p 1, 2, disjunctive syllogism
Roughly speaking, using the or connective, we are told that at least one of the statements is true, and then we are told that q is not true, so we can infer that the p must be true.