Truth functional logic preserves logical truth by substituting terms according to the rules of logic. The truth or falsity of a statement can be calculated according to the truth of its parts. For example, if A or not-A (the law of non-contradiction) is a rule, then if A is true, not-A must be false; if A is false, then not-A must be true. Compound sentences are true or false depending only on whether their components are true or false. For example, the sentence “It is raining and cold” is true if “It is raining” is true and “It is cold” is true.

Truth functional logic is typically applied according to tables that indicate the truth values of sentences that contain clauses linked by the connectives “if,” “and,” “not,” “if-then,” and “if and only if.” The truth or falsity of the whole sentence depends on the truth or falsity of its components, according to the rules of logic that apply to each of the connectives.