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Truth Table

A truth table shows the resulting value when a logical operator is used to join two propositions, forming a new, complex proposition.

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