# Lecture 5

GO TO:

## Before the Lecture

• Read Sections 2.3, 3.1 and 3.2. (Note: Look at the section Outcomes to see what you are expected to get from the reading, perhaps after also some in class help.)
• Watch the videos related to these sections (after reading them):
• Problem 2.3.1(a-c). NOTE: There is a mistake in part (c)! There is a $\in$ symbol that makes no sense. Please read the comments in the video and turn on annotations (click on the gear icon below the video window and click "On" for "Annotations") to see exactly where.
• Problem 2.3.1(d).
• Problem 2.3.10 and 2.3.11. NOTE: There is a mistake in Problem 10! On the second board I copy and $\land$ and an $\lor$, and the error carries over, resulting in an $\cup$ where there should be an $\cap$. Please read the comments in the video and turn on annotations (click on the gear icon below the video window and click "On" for "Annotations") to see exactly where.
• Problem 3.1.3.
• Problem 3.1.5.
• Problem 3.1.11.
• Problem 3.2.1.
• Problem 3.2.3.
• Problem 3.2.6.
• Write down all questions about the above topics to bring to our (online) lecture. 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

All of these are to be turned in on 06/08 by 11:59pm (Homework 2) or on 06/15 by 11:59 (Homework 3).

Section 2.3: 2, 9, 12. (Do, but do not turn in 5 and 6 and read the statements of 14 and 15).

Section 3.1: 2, 6 (state clearly what inequality property you are using/assuming), 8, 10, 15, 16.

Section 3.2: 2, 4, 7, 9, 12.

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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:

• understand families of sets (i.e., sets whose elements are sets), power sets and indexed families of sets;
• understand and know how to translate to logic statements unions and intersections of families as above;
• understand what a proof is;
• be able to write and read simple proofs;
• be able to prove simple statements of the form $P \rightarrow Q$;
• be able to prove simple negative statements (i.e., of the form $\neg P$);
• be able to use assumptions of the forms $P \rightarrow Q$ and $\neg P$ in proofs.

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