Date: Tue, 24 Aug 2004 07:16:52 -0500 (CDT) From: Mark Jacobson To: 810-080-01@uni.edu, 810-080-02@uni.edu Subject: Discrete Structures - day #1 review, day #2 preview - 810:080 Hello discrete structures students, Here below is the review note from lecture one from last fall semester's discrete class. You can consider it a review and a preview and a reading study guide for section 1.1: 1. a review of Monday's class, and 2. a preview of Wednesday's class with much that we did not get to, such as the main connective, wff (well-formed formulas, De Morgan's Laws, disjuncts and conjuncts terminology, antecedent and consequent terms, etc). Use it as a review and as a reading study guide for chapter one section 1.1. as you get ready for class #2. Note the suggestion to COMPLETELY IGNORE one confusing part of chapter one, the algorithm called Tautology Test on page 12. See you Wednesday, whether we be wet tommorrow or dry tommorrow weather-wise! Mark ---------- Forwarded message ---------- Date: Mon, 25 Aug 2003 12:38:38 -0500 (CDT) From: Mark Jacobson To: 810-080-01@uni.edu, 810-080-03@uni.edu Subject: [810-080-03] Discrete Structures - day #1 - 810:080 Hi 080 students, Please read and reread (and DO) section 1.1 of the textbook. Section 1.1 Statements, Symbolic Representation, and Tautologies We covered three binary logical operators today in class. AND A and B (A ^ B) OR A or B (A v B) IMPLIES A implies B (if A then B) (A -----> B) Can you write the truth tables for these without having to think about it? Practice that! We covered one unary operator today, the NOT operator. ' not A is written as A' or written as A ----- Propositions are combined together using logical connectives, using the above binary and unary operators. There are certain legal ways to create a compound proposition. The following is not legal, i.e. is NOT a wff: --------- (A or B)) ---> and C What is a wff? See page 6 of your textbook. What is the order of precedence for operators is wffs? There is an order of precedence for AND, OR, and NOT in all programming languages. The syntax in Java for AND is &&, ( && is double ampersand ) AND OR is || ( || is two pipe symbols ) OR NOT is ! ( ! is exclamation mark ) NOT Practice writing down the truth tables for AND, OR, IMPLIES and NOT. 1. How many rows would the truth table for each of the following wff's have? a. A and B ----> C b. (A and B) or C ----> D c. (A ---> B) and C 2. What is the main connective in each of the above problem #1 wffs? 3. What does gymnastics have to do with remembering De Morgan's Laws? See your lecture notes and page 9. 4. Why isn't "How are you doing?" considered to be a proposition? 5. Why isn't "She is a wonderful singer!" a proposition? 6. How many conjuncts are there in problem #1.a. above here? ...in problem #1.b. above here? ...in problem #1.c. above here? 7. How many disjuncts are there in all of problem #1 above? 8. What is the antecedent and what is the consequent in the following statements: If it rains today, then I will not going biking today. If you study hard sometimes, and you have the attitude it can be fun, and you study frequently then you will enjoy discrete. 9. Reread Judith Gersting's Note to the Student that occurs on the page just before Chapter 1. Look up the definition of perseverence in the dictionary. Write down the definition. She also mentions playing with the ideas in a problem. That is why one of the conjuncts stated in #8 is: you study hard sometimes --------- Playing with ideas in mathematics is just as important as perseverance. Studying math is play some of the time, and not always hard work. A casual, relaxed, playful attitude can be more effective than a stressed out, impatient attitude. 10. See the web page for our class at: http://www.cns.uni.edu/~jacobson/c080.html and see my web page at: http://www.cns.uni.edu/~jacobson/ Feel free to totally IGNORE the page 12 ALGORITHM Tautology Test! ------ If you finish reading section 1.1, go ahead and preview section 1.2. Section 1.2 Propositional Logic See you on Wednesday in class. Mark