2.1 2.2 Part1 Preview Sets: Definitions and Venn diagram I couldn't finish all. We covered till p.8 the union & intersection of three sets. I will continue next week.
2.1 Exercises 17
2.2 Exercises 29
2.2 Exercises 5,6 (for #5 and #6, draw Venn diagrams to show the identities, as done in class. The solution given in the textbook is an advanced subject that we will learn in about a month later.)
2.1 2.2 Part1 Preview Sets: Definitions and Venn diagram Go through "Set builder notations" on pp.3-4 and p.8
2.1 2.2 Part1 Preview Sets: Definitions and Venn diagram Review exercises on pp.5-6
2.2 Exercises 21 (for #21a, draw Venn diagrams to show the identities, as done in class; for #21b, first, draw Venn diagrams to show the identities; second, use Table of Set Identities and via algebraic process, as done in class. The solution given in the textbook is an advanced subject that we will learn in about a month later.)
I will send you over email a little before the recitation starts.
A quiz will be held after the recitation, during the last 10 minutes of the class.
1.1 Propositions/Statements, Logical connectives, True-False table, started. Will continue next week.
No recitation or quiz due to Dr.King's birthday makeup (Monday class meet)
Do examples and exercises appeared in the lecture files <- important!
2.1 Exercises 1
2.2 Exercises 21 (Review how it was done in class 2.1 2.2 Part2 Preview Set Identities via Venn diagram)
For #21a, draw Venn diagrams to show the identities
for #21b, first, draw Venn diagrams to show the identities; second, use Table of Set Identities and via algebraic process.
2.1 Exercises 9,11,21,29,37
8.5 Exercises 1 <- Yes, it is Section 8.5. Oddly, our textbook doesn't have an appropriate 2.1-2.2 exercise problem asking on the topic. I picked one from this later section.
2.2 Exercises 53,57,59
1.1 Exercises 38a,c,e, 11a,b,c,h, 13a--d, 17a,b,d
Recitation 2 and Quiz 2
1.1 Propositions/Statements, Logical connectives, True-False table
2.2 Part 4 Proof of Set identities (Practicing Logical equivalences in 1.3),
Do examples and exercises appeared in the lecture files <- important!
1.1 Exercises 19, 17c,h,25,29
1.2 Exercises 7
1.3 Exercises 5,7,9,11
1.3 Logical equivalences Review "Example" and do "In-class exercise" on p.10 (1.3 Math/English, Logically equiv statements, and Negation) <-- newly added on 2/5
2.2 Exercises 21a,b, 20a, 33 (HInt: Contrapositives are logically equivalent; Also, as in Tables 7 & 8 Logically equiv. involving Conditional/Biconditional Statements) --> postpone to next week
Recitation 3 and Quiz 3
2.2 Part 4 Proof of Set identities (Practicing Logical equivalences in 1.3),
1.4 2.1 Part2 Univ Exis Quantifiers (one variable), T/F statements
Do examples and exercises appeared in the lecture files <- important!
2.2 Exercises; "Prove" in the followowing problems means "rigorous proof" done in class
#21 (see pp10-11 in 2.2 Part 4 Proof of Set identities (Practicing Logical equivalences in 1.3)), #20a
2.1 Exercise #47
Do as done in class; 1.4 2.1 Part1 Predicates (one variable), Truth sets
(i) First, write the truth set using the set building notation. Include the domain and write the property of the variable(s) in English and/or standard math, as opposed to symbols of predicates such as P(x).
(ii) Next, conclude the set specifying the element in a more concrete manner, such as roster method, well-known set notations, or intervals, etc
(iii) Do your best to give a reasonable Venn diagram
2.1 Exercise #45 ("truth value" means True/False)
Do as done in class; 1.4 2.1 Part2 Univ Exis Quantifiers (one variable), T/F statements
Justify your answer T/F. If a universal statement is false, give a counter-example.
Except for obvious cases, it is usually clearer if you do (i)--(iii) in finding the truth sets, then thinking of "all " or "exist ".
Showing (i)--(iii) in finding the truth set for a predicate with the given domain will serve as a "justification" for your answer.
1.4 Exercise #37
1.4 Exercise #11
Recitation 4 and Quiz 4
No homework this week as 2/20 will be an exam.
Midterm 1
1.4 Exercise #7, 23
1.4 Example on pp.6-7 in 1.4 2.1 Part4 Variabl-ize
1.4 Supplemental Problems #1 and #2 on pp.8-11 1.4 2.1 Part4 Variabl-ize (Note that Supp Prob #1 solution has been included in the lecture file)
1.4 Exercise #41
1.5 Exercise #45 Postpone to next week
Recitation 5 and Quiz 5
1.5 Exercises #25, 27a,b,g,i, 39, 45
Recitation 6 and Quiz 6
1.7 Pt1 Lecture video1 (the last a few seconds have no audio; stop and move to the next video below)
See the lecture files 1.5 Part1 Predicate (Multi-variables) Nested Universal/Existential Quantifiers pp. 4--7 to review
how to determine T/F for a mixed quatified statements and how to justify your answer.
Recall the statement "Every non-negative real number has an multiplicative inverse."
See 1.5 Part2 Compound Nested Quantifiers, Variabl-ize pp.2--3 to review
how to express it using quantifiers, predicates, and logical connectives;
how to 'prove' that the statement is true
1.7 Exercises #1, 2,3,4, 6,7
See the analysis and steps for 1.7 proof problems from lecture note 1.7 Part1 Direct Proofs. Your solutions must follow this procedure, as done in class.
I cover Section 1.6 only as a tool for 1.7-1.8 Proofs. Hence no homework from 1.6. However, do not ignore 1.6 covered in the videos. A few basics in 1.6 will help you follow 1.7 proofs.