Deductive Logic

There are three types of deductive logic, those being Syllogism, Modus Ponens, and Modus Tollens. The first, syllogism, can be simply explained through the idea that "if A=B" and "B=C, then A=C". The two premises being made (Which would be A and B in the equation) are called the Major and Minor premises.

EX of Syllogism:

Every high school student takes math.

Johnny is a high school student.

Therefore, Johnny takes math.

Somewhat differently, Modus Ponens refer more to equations of cause and effect. The equation for a Modus Ponen could be simply put as : If A, then B. A, therefore P. This differs from syllogism because no longer is one using three variables in their logistic hypothesis. They are now stating the outcomes of a cause, and whether they happened. With syllogisms, one deduces knowledge based off of passed down facts from one subject to another with correlating ideas. With Modus Ponens, one is saying what will happen as an effect of an event, and then that the event did (or in some cases, did not) happen.

EX of Modus Ponen:

If Sara gets a date, she will go to prom.

Sara got a date, therefore she went to prom.

The third form of deductive logic is the Modus Tollen. The Modus Tollen consists of the equation, if A, then B. Not B, therefore Not A. The Modus Tollens are very similar to the Modus Ponens, yet they differ in the fact that the events did not happen, there for the effect never occured. The order of the second statement is also switched around so that one is saying the effect did not occur, therefore one can logically deduce that the cause must never have occured either. Modus Tollens are different from syllogisms similarly to Modus Ponens, in that they deal with cause and effect factors, not major and minor premises. 

EX of Modus Tollen:

If I eat, I will be full.

I am not full, therefore I did not eat.