Law of syllogism

The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form:

1. P→Q
2. Q→R
3. Therefore, P→R.

The following is an example:

1. If Larry is sick, then he will be absent
2. If Larry is absent, then he will miss his classwork.
3. If Larry is sick, then he will miss his classwork.

We deduced the final statement by combining the hypothesis of the first statement with the conclusion of the second statement. We also allow that this could be a false statement. This is an example of the Transitive Property in mathematics. The Transitive Property is many times phrased in this form:

1. A=B
2. B=C
3. Therefore A=C