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Question 1: Modus Ponens is Latin for "the mode that affirms" (UCSB.edu).

"If you have a new key to the apartment, then you can open the front door."

"You have a new key to the apartment"

Therefore:

"You can open the front door."

p→q
p ∴ q

Modus Tollens is Latin for "the mode that denies" (UCSB.edu).

"You can't open the front door."

"If you have a new key to the apartment, then you can open the front door."

Therefore:

"You don't have a new key."

¬q
p→q

∴ ¬p

Visualizing an argument is similar to solving a math problem. Math is the universal language which links all subject matter, languages and life together. There are number, variables and operations that are required in order to reach the answer or conclusion. Talking through an argument can take a long period of time and at the end the opposing side may still be unconvinced. When the argument is place in symbol form examine and trace how the variables worked together in order to justify the answer. Not every human being thinks in a precise and clear cut manner. There are some human beings that think globally or abstractly and placing the argument in symbolized form may be confusing an difficult to understand. The goal is to make the argument as clear as possible for everyone so that the presenter has a higher probability of convincing others that he or she is right.

Question 2- Imagine someone asks you what you have learned in your logic class and what you found to be the most useful information you learned there. Is it important for people to study logic? What kinds of mistakes might they make without having been exposed to a careful study of reasoning provided by logic?

Logic and common sense are similar to each other in that they are methods of reasoning used to make the best decision possible. For instance we all know that what is wet, we all know that rain is water, so it stands to reason that if we stand in the rain we are going to get wet. Logic also allows us to solve problems in progressive steps. The scientific method for instance is a set of steps that allows the experimenters or researcher to hypothesize a conclusion and then conduct an experiment to prove it's truth or error (Scientificmethod.com). Without the ability to use logic or reason human beings would believe anything and everything they are told without testing or thinking about it. Humans once believed that the world was flat and if you sailed too far in any direction you simply fell off. Through logic and reasoning humans soon found out that the world was round, and line of sight was responsible for the effect of object seeming to disappear.

Scientificmethod.com. What Is the Scientific Method? Retrieved August 2, 2011, from http://www.scientificmethod.com/sm3_whatissm.html

UCSB.edu. Modus Ponens, Modus Tollens. Retrieved August 2, 2011, from http://www.cs.ucsb.edu/~pconrad/cs40/lessons/logic/modusPonensModusTollens.html