And so on Next, we write down the premises and conclusion of the argument in the table. Then, given what you know about the truth values of the atomic statements and the truth values of compound statements composed of them, fill in the truth table. Each row in the table describes a possible truth value assignment. Row one describes a situation in which the atomic statements P and L are both true. Under that valuation, both premises are true and the conclusion is true.
L is false.
Under that valuation, the first premise is false and the second premise is true. The conclusion, this time, is false. Looking at the truth table, we see that there is no row in which the premises are true, but the conclusion is simultaneously false. We have seen a valid argument. How about an invalid one.