Modus Ponens and Modus Tollens

I was sick yesterday, so here is yesterday's homework.

Syllogisms

A syllogism is a method of reasoning that includes a minor premise, a major premise, and a conclusion. The major premise is a general statement about something, and a minor premise is another statement about a specific thing that relates to the major premise. The conclusion is the resulting idea that is formed when the minor premise is put together with the major premise to form an implication about the subject of the minor premise.

The logic of a syllogism is as follows: A=B, B=C, therefore A=C

Example:
Major premise: Emily plans to throw rotting bananas at all people who make stupid polls.
Minor premise: Both Aaronito and Amanda made stupid polls.
Conclusion: Emily plans to throw rotting bananas at Aaronito and Amanda.

Modus Ponens is a syllogism that states:
If P, then Q.
P.
Therefore, Q.

P is a condition, that if fulfilled, will lead to Q.

Example:

If a unicorn trots in front of me and eats this acorn in my hand (P), then I will grow a cornfield (Q).
A unicorn just trotted in front of me and ate the acorn in my hand. (P is fulfilled)
Therefore, I will grow a cornfield. (Q takes place as a result of P).

Modus Tollens is another form of syllogism, similar to Modus Ponens, but it states that if something does not take place, then something else will also not take place. If the condition P is not fulfilled, then Q will not take place.


Example:


If Elmo does not give me a free pair of pajamas (P), then I will not eat another cookie for the rest of my life (Q).
Elmo did not give me a free pair of pajamas (P).
Therefore, I will not eat another cookie for the rest of my life (Q).