Announcements and reminders:
- Today we will have another badges quiz with sets badges. The badges are:
- Sets I: basic definitions (set, element, equality, empty, cardinality)
- Sets II: operations (union, intersection, difference, universe, complement, Venn diagram)
- Sets III: Set-builder notation
- Sets IV: ordered pairs, Cartesian products and powers, subset and powersets, including cardinality
- Logic IV: negating statements
- Proofs I: setting up a proof by contradiction
- The new groupwork has been posted. I will go one more week before remixing groups, but as always, contact me if you have trouble scheduling 2 hours or any other problem. If you have 6 people in one group, consider breaking into two groups of 3.
For today’s class:
- We will mostly focus on proofs by contradiction today. (The Logic IV and Proofs I badges are relevant to the study of proof by contradiction, so they will begin to be available on the badges quizzes.)
- Bring your homework about “threeven” that was assigned in the previous daily post.
- Read Hammack, page 111 (the first page of Chapter 6), and from page 113 to the end of Section 6.2 on page 116. In a couple spots, there’s a bit of notation from Boolean Logic in this chapter, because Hammack assumes we have covered Chapter 2 before getting to Chapter 6. Consider it an exercise in adaptive reading — just work around the notations you don’t know. We will be working on Boolean Logic soon, and for now skipping over his reference to it still leaves a very useful reading.
- Study for the Badges Quiz. My advice: look your scores up on canvas, look over your returned quiz, and decide on 2 or 3 badges you’d like to focus on getting full credit for this week. (Study a few excellently, instead of all of them passably.) To study, it is helpful to find the relevant material in Hammack and do exercises (odd answers are in the back) to brush up on the concepts. If you have questions about the badges quiz material, I can take them up at the beginning of class Monday before we do proof by contradiction.