A logical argument consists of one or more premises, propositions that are assumed to be true, and a conclusion, a proposition that is supposed to be guaranteed to be true (as a matter of pure logic) if the premises are true. For example, the following is a logical argument:

•       p → q

•       p

•       Therefore, q.

This argument has two premises: p → q, and p. The conclusion of the argument is q. If a logical argument is valid if the truth of the premises guarantees the truth of the conclusion; otherwise, the argument is invalid. That is, an argument with premises p₁, p₁, … p_n and conclusion q is valid if the compound proposition

(p₁ & p₂ & … & p_n) → q

is logically equivalent to TRUE. The argument given above is valid because if it is true that p → q and that p is true (the two premises), then q (the conclusion of the argument) must also be true.