Week 1:

- Truth Tables, Tautologies, and Logical Equivalences.
- Quantifiers and Negation
- Homework (due Thursday)
- Writing Proofs (WP) and Organize Proofs (OP).

- Definitions for sets (Today's handout (Jan 14) plus I added answers to the three homework questions that were due today).

Test 1 with answers to questions 1 through 4 (for number of points for each question, click here). For next class, study these answers, and turn in question 5 if you haven't already.

Your HW for Thursday Feb 20 is: Read/watch/study the following handouts, then give two proofs for the first part of exercise 5 in section 2.2 (see the last handout for hints):

- View: Hotel infinity.
- Study: Overview of section 2.1.
- View this excellent youtube video about Cardinal numbers and Ordinal numbers. It is solid mathematically, and a joy to watch. (The book covers Cardinal numbers in Chapter 2, and Ordinal numbers in Chapter 3, but we will skip much of Chapter 3 to spend more time on Chapter 4).
- To prepare for Thursday's class view: ZFC Axioms of Set Theory: complete(!) list of all statements that mathematicians accept without a proof.
- Study items 1-19 in List of facts for Chapter 2. A shortened version of this list will be printed with test 2, this way you can use the definitions without having to memorize them. If you are used to using this list for your homework, then that will benefit you in test 2.
- Turn in this homework on Thursday Feb 20.
- Study this handout how (not) to prove that a function is onto which addresses problems in Tuesday's quiz.

Sample for test 2 (Do Ex 2, 3, 5. Turn in Ex 3) and more sample questions for test 2 (turn in Ex 6, 7, 8). Also do (not yet turn in): 2.4 Ex 1 and 2.

Some of the theorems in the book have very hard proofs, as you may have noticed
in class today. Our next focus will be on **how to use the theorems**. Here it no longer matters
that the proof was hard, as long as a proof exists, we are allowed to use these theorems.
To make these theorems easier to use, they will be included in the test in the "list of facts".

Many of the exercises are designed to **test if you can use** these theorems. For many exercises, the proof either

- (a) uses the right theorems (the right items in the list of facts),
- (b) or is ridiculously hard,
- (c) or is wrong.

In test 1 the goal was to learn how to compute with statements.
In test 2 the goal is to learn **how to use statements**. That's why it is so important
to cite the right item in each non-trivial step. Please do that in your HW and in the test.

You can write diagrams in your scratch paper, but don't include them in your HW. Instead of diagrams or other intuitive explanations, you should justify each step in your answer by citing which item (from the list of facts) justifies that step.

Answers for: Sample for test 2 and more sample questions for test 2.

More sample questions: test 2 Fall 2019 and answers.