A proposition is a statement which is either true or false. In propositional logic<\/a>, we take propositions as basic and see what we can do with them. Since this is mathematics, we need to be able to talk about propositions without saying which particular propositions we are talking about, so we use symbolic names to represent them. We will always use lowercase letters such as and to represent propositions. A letter used in this way is called a propositional variable<\/a>. Remember that when I say something like \u201cLet p be a proposition,\u201d I mean \u201cFor the rest of this discussion, let the symbol p stand for some particular statement, which is either true or false (although I am not at the moment making any assumption about which it is).\u201d The discussion has mathematical generality in that p can represent any statement, and the discussion will be valid no matter which statement it represents.<\/p>\n What we do with propositions is combine them with logical operators. A logical operator can be applied to one or more propositions to produce a new proposition. The truth value of the new proposition is completely determined by the operator and by the truth values of the propositions to which it is applied.1 In English, logical operators<\/a> are represented by words such as \u201cand,\u201d \u201cor,\u201d and \u201cnot.\u201d For example, the proposition \u201cI wanted to leave and I left\u201d is formed from two simpler propositions joined by the word \u201cand.\u201d Adding the word \u201cnot\u201d to the proposition \u201cI left\u201d gives \u201cI did not leave\u201d (after a bit of necessary grammatical adjustment).<\/p>\n