Deductive Logic

Today, we went over the three types of Deductive Logic, which are:

1. Syllogism
2. Modus Ponens
3. Modus Tollens

1. Syllogism is a deductive reasoning where a major premise (which contains A term and B term) and minor premise (which contains B term and C term) combine to make a conclusion (which contains A term and C term).

Similar to the transitive property in geometry
(If A=B, and B=C, then A=C).

• example:

Major premise: All girls with big, googly eyes are attractive.
Minor premise: Misty has big, googly eyes.
Conclusion: Misty is attractive

• example:

Major premise: My parents are Santa Claus.
Minor premise: My parents are real
Conclusion: Santa Claus is real

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2. Modus Ponens is a deductive reasoning where a "if p, then q" statement is given and "p" is given as a positive premise, so that we may be sure of the positive premise of "q".

If p, then q
p
-------------
therefore, q

• example:

If Bruce is hungry, then he can eat a whale
Bruce is hungry
-------------
therefore, he can eat a whale

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3. Modus Tollens is a deductive reasoning where "if p, then q" statement is given and "q" is given as a negative premise, so that we may be sure of the negative premise of "p"

If p, then q
not q
-------------
therefore, not p

• example:

If Bruce was a good boy, then Santa will get him an iTouch for Christmas.
Bruce did not get an iTouch for Christmas
-------------
Therefore, Bruce was not a good boy.