# Law of Detachment

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

## Meaning

Law of detachment:

If a conditional (*p* → *q*)

and its hypothesis (*p*) are true,

then its conclusion (*q*) is true.

Recall the truth value of a conditional statement:

If *p* and *p* → *q* are both true,

then there's only one case for *q*: true.

## Example

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

It says *p* → *q* and *p* are true.

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