Conjunctions and disjunctions are types of compound propositions found in propositional logic. A conjunction is true only if both of its component propositions are true. A disjunction is true if at least one of its component propositions is true.
One way to evaluate compound propositions is to use a truth table. A truth table lists the four possible outcomes that can occur with two propositions. For example, if there are two statements A and B, the four possible combinations are: A and B are both true, A is true and B is false, A is false and B is true, and A and B are both false. A conjunction is true in the first case, when A and B are both true, and is false in the other three cases. A disjunction is true in the first three cases and is false only in the last case, when A and B are both false.