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.