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 questions about the sections covered.
- 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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