The three forms of logic are deductive, inductive and abductive reasoning. Deductive logic is the reasoning behind mathematics; it begins with a true and asserted general rule and then proceeds to a specific application or conclusion. Inductive reasoning begins with a specific observation that is limited in its scope and then proceeds to a larger general conclusion, and abductive reasoning begins with partial set of observations and attempts to formulate what may be the most likely explanation.
Deductive reasoning is the most obvious and trusted form of logic. An example of deductive reasoning is the following: If X equals 7 and if Y equals 3, then 3 times X plus Y equals 24. The reasoning proceeds from a given and true premise, in this case, X equals 7 and Y equals 3, and then leads to a conclusion that must be true as a result of logical necessity.
In a nonmathematical setting, an example of deductive logic is the following progression from a major premise, to a minor premise and then to a final conclusion: All humans breath oxygen, John is a human and John, therefore, breathes oxygen. This form of deductive reasoning is also known as a syllogism.