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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.

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    I fear there's a bit of information one needs to make this a legitimate proof: why do you suppose $A \lor B$? Perhaps with the proper motivation (i.e., context), we could help you understand the proof. – 2017-01-14
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    It seems likely that whomever listed these statements was identifying the first three items there as premises (assumptions). If $¬ B$ is a premise, then you are assuming the logical negation of $B$. – 2017-01-14

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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 $\therefore D$.

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    Sweet, I think this makes more sense now. Thank you. – 2017-01-16
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dictionary.com defines:

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