Question about reading proof notation

Question

When reading the following problem, do you assume that each premise is true? So since number 2 states ¬ B am I to assume that ¬ B is true? Which would mean B is false?

1. A ∨ C → D Premise
2. ¬ B Premise
3. A ∨ B Premise
4. A 2, 3, Disjunctive Syllogism
5. A ∨ C 4, Addition
6. D 1, 5, Modus Ponens QED.

Thanks for the help.

Answer 1

Yes, you can take premises as taken to be "true" (assumptions taken as given) from which you are to derive the conclusion. So given the premise $\lnot B,$ any assertion $B$ would lead to a contradiction.

So in your example, given $A\lor B$, and given $\lnot B$, we appeal to the rule of inference called disjunctive syllogism to warrant (justify) the deduction$A$.

From the deduced $A$, we use addition to "add" $A \lor C$ (since if A is logically deduced from accepted premises, and thus taken as true, so must $A\lor C$ be inferred.

Then, by modus ponens with the first premise and the inferred $A\lor C$, we conclude $\therefore D$.

Answer 2

dictionary.com defines:

'Premise': a statement which is assumed to be true for the purpose of an argument from which a conclusion is drawn