Lecture 3

Navigation

• Back to Main Page.
• Back to the Lectures.
• Before the Lecture
• Related Problems
• In Class
• Outcomes

Before the Lecture

• Read the rest of Section 1.5 and 2.1-3. (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 this section (after reading it):
  • Remarks on Section 1.5.
  • Problem 1.5.2.
  • Problem 1.5.6.
  • Problem 1.5.10.
  • Remarks on Section 2.1.
  • Problem 2.1.2.
  • Problem 2.1.5.
  • Problem 2.1.7.
  • Remarks on Section 2.2.
  • Problem 2.2.1.
  • Problem 2.2.8.
  • Problem 2.2.9.
  • 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.
• 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.

 

Related Problems

The "turn in" problems are due on 06/14 (Homework 2) by 11:59pm.

Section 1.5:	Turn in: 5, 9.
	Extra Problems: 3, 4.
Section 2.1:	Turn in: 6.
	Extra Problems: 3, 5.
Section 2.2:	Turn in: 2(b-c), 7.
	Extra Problems: 2(a), (d), 5, 10.
Section 2.3:	Turn in: 2(c), 12(a-b).
	Extra Problems: 2(a-b), (d), 5, 6, 9, 12(c). (Also, take a look at the statements of 14 and 15.)

 

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.

 

Outcomes

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

• know the truth table of if/then operation (Problem 1.5.4);
• know that $P \rightarrow Q$ is equivalent to $\neg P \vee R$;
• know the contrapositive and converse of if/then statements;
• translate statements with if/then from common speech to logical symbols (Examples 1.5.1, 1.5.3, Problem 1.5.3) and vice-versa;
• simplify and establish equivalency of statements involving if/then (Example 1.5.2, Problems 1.5.5, 1.5.9);
• understand and know how to use quantifiers, including multiple nested quantifiers (Examples 2.1.1, 2.1.4);
• translate statements with quantifiers from common speech to logical symbols (Examples 2.1.2, 2.1.3, Problem 2.1.3) and vice-versa (Problem 2.1.5);
• know how to restate negation of quantified statements in positive form (Problem 2.2.2);
• understand and know how to used bounded quantifiers and how to negate them;
• know the ``distributive law'' for quantifiers (pgs. 70 and 71);
• 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 (most problems from 2.3).