An argument is a statement of the form \[P_1 \wedge P_2 \wedge \dots \wedge P_n \rightarrow Q\] The statements \(P_1, P_2, \dots, P_n\) are the premises, and the statement \(Q\) is the conclusion.
In practice, an argument starts with a set of assumptions \(P_1, P_2, \dots, P_n.\) One shows that if \(P_1\) and \(P_2\) and \(P_3\) and so on up to \(P_n\) are all true, then \(Q\) is true. However, there are often other statements derived from \(P_1, P_2, \dots, P_n\) before concluding \(Q.\)
An argument \[P_1 \wedge P_2 \wedge \dots \wedge P_n \rightarrow Q\] is valid if it is a tautology. This means that when all the premises are true, the conclusion is true. If some premises are false, then the conclusion can be true or false.