Suppose the two propositions being joined are P and Q. Each of these propositions will have two possible truth values: true, or false. This gives us four possible combinations. These are represented on a table, as follows:
In the space to the right, a complex proposition is displayed. Beneath the complex proposition are the truth values which result given the four possible truth values of P and Q. For example, here is the truth table for the complex proposition P and Q:
Notice that the complex proposition may be true or false depending on the different truth values of P and Q. Thus, if we know what the truth values of P and Q are, we know what the truth value of P and Q is.
17 August 1996