Deductive Reasoning

There are three types of Deductive Reasoning

1. Syllogism
2. Modus Ponens
3. Modus Tollens

SYLLOGISM

Syllogism consists of a major premise and a minor premise that combine to establish a conclusion.
Each premise consist of terms:

• Major Premise (A and B)
• Minor Premise (B and C)
• Conclusion (A and C)

Ex: B A
Dogs love to play.
C B
Toby is a dog.
C A
Therefore, Toby loves to play.


MODUS PONENS

Modus Ponens is a form of deductive reasoning where if the statement "if p, then q" is valid,
and if p is a positive premise, then q must also be a positive premise. This rule can also be reversed and used in the negative. If p is a negative premise, then q must also be a negative premise.

Ex 1: p q
If he aces the test, then he will ace the class.
p
He aced the test.
q
Therefore, he aced the class.

Ex 2: p q
If he doesn't ace the test, then he will not ace the class.
p
He did not ace the test.
q
Therefore, he did not ace the class.


MODUS TOLLENS

Modus Tollens is a form of deductive reasoning where if the statement "if p, then q" is valid, and q is a negative premise, then p must also be a negative premise. If there is "Not q", then therefore there is "Not p".

Ex: p q
If he washes his car, then it will be clean.
q
It is not clean.
p
Therefore he did not wash his car.