Logic: can be defined as the are of reasoning. A statement which is either true or false but not both. We shall assume that a large class of statements and to each one w can attach a name. We use the letters a, b, c, ... p, q, r, s, ... to denote propositions e call them propositional variables. The equivalent statements of P and q are joined by grammatical conjunctions Syllogism is a conclusion in logic from two given statements. Two propositions are equal if they have the same truth values. To prove equality of two purposes the general method is to construction their truth tables. Tautology: A proposition which is always true no matter what truth values are assigned to its component propositions.