## Before the Lecture

• Read Section 3.5-6 and 4.1-2.
• Watch the videos related to this section (after reading it):
• Write down all questions about the above topics to bring to our (online) lecture. (You can also type them in the file "Questions.tex" in Sage Math Cloud.) Comments about the videos are welcome!
• Work on the assigned problems for these sections. (See Related Problems below.) You don't need to finish them, but try to work on as many as you can and the bring your questions to class.

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## Related Problems

The "turn in" problems are due on 06/21 (Homework 4) by 11:59pm.

 Section 3.5: Turn in: 8, 21. Extra Problems: 9, 13, 17. Section 3.6: Turn in: 10. Extra Problems: 2, 7. Section 4.1: Turn in: 9, 10. Extra Problems: 3, 7. Section 4.2: Turn in: 5, 8. Extra Problems: 2, 3, 6(b).

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## In Class

In class:

• We will discuss the reading and pace.
• I will discuss the main points.
• I will answer any other questions.
• We can work on the HW problems.

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## Outcomes

After the assignment (reading and videos before class) and class, you should:

• know how to prove a statement with an "or" in the conclusion (Examples 3.5.2, 3.5.3, Problem 3.5.8);
• know how to prove a statement with an "or" in the premise (Example 3.5.1, Problem 3.5.17);
• understand the "there exists a unique" quantifier, including how to write it without using the $\exists !$ symbol;
• know how to negate a statement of the form "$\exists ! x \; (P(x))$";
• know how to prove "there exists a unique" statement (Example 3.6.2, all problems from 3.6);
• understand ordered pairs and Cartesian products;
• know how to prove statements involving set operations of Cartesian products (Theorem 4.1.3 and Problems 4.1.9 and 4.1.10);
• know how to find truth sets of statements in more than one variable (Example 4.1.6 and Problem 4.1.3);
• understand what a relation is;
• understand domains, images, inverses and compositions of relations and be able to prove statements involving these;

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