Deductive reasoning is reasoning that goes from the general to the specific or particular. In a way, it is the opposite of inductive reasoning, which goes from the particular to the general. Deductive reasoning, if done properly, results in conclusions that are said to have deductive validity. In such an argument, it is impossible for the premises to be true and the conclusion to be false.
In contrast with inductive reasoning, in deductive reasoning no new information is added; the conclusions are, in a sense, already implicit in the premises. For example, with the premises "Socrates is a man" and "All men are mortal" you might conclude that "Socrates is mortal", but how do you know that "All men are mortal" unless you already know that "Socrates is mortal?"
Mathematics makes heavy use of deductive reasoning. All mathematical theorems are proved using deductive reasoning.
There are several kinds of deductive reasoning, including propositional logic and syllogistic logic.