Deductive Logic

Syllogisms, Modus Ponens, and Modus Tollens are all examples of deductive logic.

Syllogisms
All CORE students are lazy.
Erika is a CORE student.
Erika is lazy.

A syllogism consists of the major premise, the minor premise, and the conclusion. Each of the premises has one term in common with the conclusion. Here, the "formula" a=b, b=c, therefore c=a can be used to describe Erika; a being All CORE students, b being lazy, and c being Erika.

Modus Ponens
If I do my homework, I'll pass biology.
I do my homework.
Therefore, I'll pass biology.

Modus Ponens can be summarized by:

If p, then q
p
Therefore, q
Like cause and effect, q will happen if p happens.

Modus Tollens
If I eat that donut on the table, I'll feel fat.
I don't feel fat.
Therefore, I didn't eat that donut on the table.

Modus Tollens can be summarized by:
If p, then q
not q
Therefore, not p
If premise p is true, then premise q is also true. Premise q us false, therefore premise p must be false. Unlike Modus Ponens, the second and third statements in Modus Tollens are negated.