In mathematics, a proposition is a statement which must be proved by a deductive argument in order to be considered true. Propositions are also called theorems. In general, mathematical propositions have the logical form "If p, then q" where p and q may be definitions, axioms, or other propositions. The "p" part of the proposition is called the hypothesis and the "q" part is called the conclusion. For example, in the proposition "If two integers are both odd, then their product is odd," the hypothesis is "two integers are odd" while the conclusion is "their product is odd." When written in everyday English, propositions may not literally have the "If p, then q" form. For instance, the proposition of the preceding sentence would usually be stated as "The product of any two odd integers is odd." The point is that if a statement in English is truly a...