Law of Detachment

Law of Detachment

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

Meaning

If a conditional and its hypothesis is true, then its conclusion is true.

Law of detachment:
If a conditional (pq)
and its hypothesis (p) are true,
then its conclusion (q) is true.

Recall the truth value of a conditional statement:

If p and pq are both true,
then there's only one case for q: true.

Example

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

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

It says pq and p are true.

Then, by the law of detachment,
q is true: I'll stay home.