Can a conditional statement have multiple premises? Is it correct to say that a conditional statement of the form p ^ q -> r has multiple premises (where the premises are the individual conjuncts p and q) or is that an incorrect use of the term "premise" when referring to implications (as the conjunction itself could be considered the only "premise" of the implication)? I ask because, in Rosen's Discrete Mathematics and its Applications, he claims that "A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion". I am unsure whether he is referencing the premises and conclusion of the universally quantified conditional statement or the premises and conclusion of something else, such as the premises assumed to be true so that the theorem can be concluded.
 A: In that passage, Rosen is undoubtedly using 'premises' to refer to the conjuncts that make up the antecedent of the conditional, while the 'conclusion' would be the consequent.  This is unusual terminology, since in the context of a conditional we typically talk about antecedent and consequent, but at the same it is understandable: when you prove a conditional, you typically use the antecedent as the premise (or, if the antecedent is a conjunction, you take the conjuncts as the premises), and the consequent as the conclusion of your proof/argument. And note that Rosen is indeed talking about 'theorems' in this passage, so that makes sense ... But yeah, I am with you: technically his language is a little off
A: To prove a mathematical theorem you assume your premise and do your best to get to the conclusion. Very often, the premise you are assuming that's true contains a lot of claims. If you let each of those claims be a logical letter such as p,q, and so on, you'll get the structure that you're asking, a "multiple premises".
