Law of Syllogism

Law of Syllogism

How to use the law of syllogism to solve logic problems: meaning, example, and its solution.

Meaning

If 'if p then q' is true and 'if q then p' is true, then 'if p then r' is true.

Law of syllogism:
If pq and qr are both true,
then pr is true.

Example

The given statements are true: If it's raining, then I'll stay home. If I stay home, then I'll call you. Write a true statement that can be derived from the given statements.

p: It's raining.
q: I'll stay home.
r: I'll call you.

It says pq and qr are both true.

Then, by the law of syllogism,
pr is true:
If it's raining, then I'll call you.