Both Section 2-4 of the Glencoe text and Section 13-1 of the U of Chicago text mention two laws that are important to logical thinking. Both texts call the first law the "Law of Detachment," which states that from

*p*and*p*=>*q*, conclude*q*. This law was mentioned in my geometry text 20 years ago, except it was in the back rather than in the main text, and called by its Latin name,*modus ponens*.
The second law has different names in the two texts. The Glencoe text calls it the "Law of Syllogism," and states that it is sort of like a transitive property for logic. Therefore, the U of Chicago calls it the "Law of Transitivity." From

*p*=>*q*and*q*=>*r*, conclude*p*=>*r*. But two British logicians, Bertrand Russell and A.N. Whitehead, used the name "Syllogism" about a hundred years ago.
Even though there are many laws in logic, these two are by far the most important. In fact, the Metamath website -- a site that seeks to write two-column proofs for many math theorems, calls the Law of Syllogism the most commonly used assertion, followed by Detachment (

*modus ponens)*:

My student had a little trouble at first distinguishing the two, but by the end of our session he was getting the hang of it. I can see why Glencoe would place this before beginning proofs. I'm not sure why the U of Chicago waits until Chapter 13 to present this information. That one may want to delay indirect proofs until Chapter 13 is understandable, but I don't know why this lesson is in Chapter 13 while converses -- a related logical concept -- appear in Chapter 2. I had no worksheet of mine to show my student, since I'm nowhere near writing a worksheet for Lesson 13-1 yet.

Instead of Chapter 13, let's think about Chapter 6 instead. We have just about finished Chapter 6, and so let's get ready for a test. The following worksheet is intended as a review for the upcoming test on the material of Chapter 6. As usual, I base my problems on the SPUR section of the U of Chicago text, and this review worksheet may contain repeats from the Chapter 6 quiz.

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