In everyday language we often claim that certain statements oppose or disagree with one another. We claim some sentences mean the same thing, or are equivalent to one another, but the manner in which we do this is imprecise. We make statements such as “All people love Elvis” and, when someone else claims that “No people love Elvis” we assume that the statements are contradictory, but we do not really have a clear definition of what “contradiction” means. From a logical perspective, statements about the same subject matter can either oppose one another or be equivalent to one another. We will begin by examining opposition. Statements can oppose one another in one of four ways: they can be contradictory, contrary, subcontrary, or alterns. For
