Math 131 - Discrete Mathematics
-- Fall 2024 Assignments and Tasks
- My teaching style is very adaptive, so I only post class assignments and tasks as we become ready to cover that material.
- These are labeled Preliminary before class.
- AFTER class, I adjust the list to accommodate for any flexing we did DURING class that day, and mark the listing Confirmed.
-
Listings go in order of most RECENT date on top.
*** WEEK FIVE IS BELOW ***
Wednesday, Sept. 25, posting will appear later this week. It will include the HW list that will be due MONDAY.
- Exam #1 is NEXT CLASS, Friday, Sept. 27. (link opens Topics List)
- CONFIRMED From Monday, Sept. 23, 2024 - Logic: Truth Values for Multiple Quantifiers
- Study your notes and Activity #6.
- Solutions to the Activity are in D2L Content.
- Read/reread: Section 3.3 pp.84-87 and p.91 through end of Section.
- There is no HW due until next Monday, Sept. 25.
- Here are some practice problem with multiple quantifiers: Exer. Set 3.3 (p.93) #10, 41, 46-49, 53, 54 - and INFORMALLY justify all of these
- Exam #1 is Friday, Sept. 27. (link opens Topics List)
*** WEEK FOUR IS BELOW ***
- CONFIRMED For Friday, Sept. 20, 2024 - Logic: Tarski's World for Quantified Statements
- Study your notes and Activity #5.
- Solutions to Activity #5 are posted in D2L Content.
- Read/reread the info listed for Wednesday, Sept. 18.
- HW #11 is due in class on MONDAY, Sept. 23: Do all tasks below.
- Exer. Set 3.1 (p.73): #9-12, giving the value of your counterexample AND showing that it makes the algebra wrong
- Exer. Set 3.1 (p.73):
#27, giving the same four types of answers (i)-(iv) as on Activity #5
- Exer. Set 3.1 (p.73): #28-30, writing as informal statements, then support true/false answers with examples and counterexamples where appropriate, but only INFORMAL justifications where it's impossible to exhaust an infinite domain
- One way to define the term "real number" is that it's a number that can be written using decimal notation.
- Exam #1 is next Friday, Sept. 27, in class. (Link opens Topics List)
- CONFIRMED For Wednesday, Sept. 18, 2024 - Logic: Tarski's World for Quantified Statements
- Study your notes and Activity #5.
- Read/reread:
- Section 3.1: Definition and Example 3.1.3 on p.65
- Section 3.1: Definition and Example 3.1.4 on pp.66-67
- Section 3.1: p.72
- Beware that the solutions to parts (a) and (d) of Example 3.1.13 do NOT exhaust the domain.
- I would not award full credit for them: I require that we exhaust the domain.
- So (a) should read "This statement is true. All the triangles - a, c, and g - are blue."
- (d) should read "This statement is false. All the squares - e, h, and j, - are either blue or black."
- There is NO HW #10 due Friday (Sept. 20). Instead, everyone earns 10/10 for completing Activity #5.
- CONFIRMED For Monday, Sept. 16, 2024 - Logic: Negating Quantified Statements
- Study your notes and Activity #4.
- Solutions to Activity #4 are posted in D2L Content.
- Read:
- Section 3.2 pp.76-78
- Section 3.3 p.90 starting with "Negations of Multiply Quantified Statements" up TO "Order of Quantifiers" on p.91
- HW #9 is due Wednesday: Do ALL tasks below. (The list is shortened from what I displayed in class.)
- Exercise Set 3.2 (p.82):
- #1-4 (AVOID the words "none" and "no" in these.)
- #9-10, 16-19
- Exer. Set 3.3 (p.92): Negate the following from their original form - do NOT follow the book's instructions:
- #13-19, 49, 50, 52-53 (for 52-53, the ``and'' is grammatical, creating a list, so don't negate it)
*** WEEK THREE IS BELOW ***
- CONFIRMED From Friday, Sept. 13, 2024 - Logic: Intro to Quantified Statements
- Study your notes.
- Read CAREFULLY: The reading is crucial this time!
- Section 1.2: p.8 just down to the blue box
- Section 3.1: pp.63-70
- You should also review our work with formal/informal from Day 1.
- HW #8 (EIGHT!) is due in class on Monday, Sept. 16:
- Exer. Set 3.1 (p.73): #1-5, 7, 13-15, 16ab, 17, 21, 23, 24
- Note: in #15, you're to avoid quantifier notation. Quantifier words are okay to still use.
- CONFIRMED For Wednesday, Sept. 11, 2024 - Logic: Biconditional Statements, Prereqs for Quantified Statements
- Study your notes.
- Read/reread Section 2.2: pp.43-47.
- HW #7 is due in class on Friday, Sept. 13:
- Exer. Set 2.2 (p.48): #32, 33 as conjunctions in TWO different ways, as in class
- Exer. Set 2.2 (p.48): 40, 41, 44, 45
- Exer. Set 3.2 (p.82): #39-42
- Extra: Negate the statements in #32, 33 from p.48.
- Extra: Create a truth table demonstrating that p<->q is logically equivalent to (p->q)A(q->p).
- CONFIRMED For Monday, Sept. 9, 2024 - Logic: Conditional Statements (part 2)
- Study your notes and Activity #3.
- Solutions to Activity #3 are posted in D2L Content.
- Read:
- Section 2.2 pp.42 through end of Example 2.2.8 on p.44.
- Xeroxed selection "Synonyms" from Smith/Eggen (handed out and in D2L Content)
- HW #6 is due in class on Wednesday, Sept. 11:
- Exer. Set 2.2 (p.48): #22abdef, 23abdef, 24-26, 46
- Hint: #46 is first making you determine which statements are converses, inverses, or contrapositives.
- Then you have to apply what you know about logical equivalence from Problems #24-26.
- Supplemental Problems
*** WEEK TWO IS BELOW ***
- CONFIRMED From Friday, Sept. 6, 2024 - Logic: Conditional Stmts
- Study your notes and Activity #2.
- Solutions to the Activity are posted in the D2L Content area (in the Solutions to... submodule.)
- Read Section 2.2:
- pp.38-40
- p.41 starting with "The Negation of a Conditional Statement" through the sentence "It is tempting..." just below the top Solution on p.42
- Blue box on p.44 through Order of Operations box atop p.45
- HW #5 is due MONDAY, from Exer. Set 2.2 (p.48): #5-10, 15-21
- #21 should NOT need a truth table, so don't make one.
- Problems #16-18 combine several skills we've worked on this past week:
- You will convert from verbal stmts to stmt forms using variables (p,q,r, etc.) and the logic symbols we now know (as in HW #2)
- Then, you will ALSO use a truth table to decide logical equivalence, and explain your yes/no answer in a sentence (as in HW #3).
- You MUST actually spell out what stmt each of your variables means, such as writing p= You paid full price. Don't assume I automatically know.
- CONFIRMED From Wednesday, Sept. 4, 2024 - Logic: De Morgan's Laws
- Study your notes
- Read:
- Section 2.1: p.32 through end Example 2.11 on p. 34, plus Theorem 2.1.1 p.35
- Order of Operations on top p.45 (negations attach to the "closest" item ONLY)
- HW #4 is due FRIDAY:
- From Exer. Set 2.1 (p.36): #25-39
- Extra: Create a truth table to show that ~(pVq) is logically equivalent to (~p)A(~q) but NOT equivalent to (~p)V(~q). As in previous HW, explain your results in a sentence.
- See Announcements section at the end of this web page for reminders about format for HW.
*** WEEK ONE IS BELOW ***
- Confirmed For Friday, Aug. 30, 2024 - Logic: Statement Forms and Basic Connectives (continued)
- Study your notes
- Read/reread Section 2.1:
- pp.27 beginning at "Truth Values" through end of p.31
- "Tautologies and Contradictions" on p.34 through end of section
- HW #3 is due next WEDNESDAY:
- Exer. Set 2.1 (starts on p.36):
- #12-15, 16, 18-20, 22, 23 (make one truth table per problem)
- The word "and" you see is just part of the author's instructions; it's NOT a "logic and."
- Also, bold t's and bold c's do NOT change their truth values ever - they are logic constants, not variables. Put them AFTER your p, q, r, etc.
- #40, 42, 43
- See Announcements section at the end of this web page for reminders about format for HW.
- Confirmed
For Wednesday, Aug. 28, 2024 - Logic: Statement Forms and Basic Connectives
- Study your notes.
- Read Section 2.1 from bottom p.24 ("Statements") through end p.29.
- HW #2 is due FRIDAY:
- Exer. Set 2.1 (starts on p.36):
- #5, 6-8, 10, 11
- #32, 33, 36, 37 - IGNORE instructions to negate; instead rewrite using "and," "or" as on p.26
- Supplement to HW #2 - also staple this page to the BACK when you hand in your assignment
- See Announcements section at the end of this web page for reminders about format for HW.
- Confirmed For Monday, Aug. 26, 2024 - Formal/Informal Statements
- Study your notes and Activity #1.
- My written solutions to the Activity are in D2L Content.
- Review the Syllabus thoroughly.
- Read Section 1.1 (pp.1-5) CAREFULLY.
- Beginning with "Some Important Kinds of Mathematics Statements" on p.2, the statement NAMES aren't important yet, but the examples ARE!
- A scan is in the D2L Content area if you don't have access yet.
- HW #1 is due WEDNESDAY: See the Announcements below for more info.
- Exer. Set 1.1 (starts on p.5): #1-13
- For fill-ins, match the style - formal versus informal - that the statement starts out as.
- This assignment is unusually short; most will be about double this length.
- Announcements:
- When doing HW, write on your own paper, with your name, date, and HW # on the first page.
- Leave room for me to write feedback, staple, and remove ragged edges.
- We can go over 1-3 questions at the start of class, before you turn the HW in.
- However, you should NOT be scrambling to complete other problems during that time.
- If you're having trouble, see/email me or attend Laura's tutoring BEFORE HW is due; don't just wait until class time.
Dr. J. Lyn Miller, Mathematics and Statistics, Slippery Rock University