Law of Syllogism

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

(1) If p, then q.

(2) If q, then r.

Then we can derive a third true statement:

(3) If p, then r.

 

Example:

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

1) If it snows today, then I will wear my gloves.

2) If I wear my gloves, my fingers will get itchy.

Let p be the statement "it snows today", let q be the statement "I wear my gloves", and let r be the statement "my fingers get itchy".

Then (1) and (2) can be written

1) If p, then q.

2) If q, then r.

So, by the Law of Syllogism, we can deduce

3) If p, then r

or

If it snows today, my fingers will get itchy.