# Law of Detachment

In mathematical logic, the Law of Detachment says that if the following two statements are true:

(1)
*
If
$p$
, then
$q$
*
.

(2) $p$

Then we can derive a third true statement:

(3) $q$ .

**
Example:
**

If the following statements are true, use the Law of Detachment to derive a new true statement.

1) If you are a penguin, then you live in the Southern Hemisphere.

2) You are a penguin.

Let $p$ be the statement "you are a penguin", let $q$ be the statement "you live in the Southern Hemisphere".

Then (1) and (2) can be written

1) If $p$ , then $q$ .

2) $p$ .

So, by the Law of Detachment, we can deduce that $q$ is true. That is,

You live in the Southern Hemisphere.