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 Syllogism 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.