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CS 173: Discrete Mathematical Structures

CS 173: Discrete Mathematical Structures. Cinda Heeren heeren@cs.uiuc.edu Rm 2213 Siebel Center Office Hours: M 4:30p, T 1:30p. CS 173 Discrete Mathematical Structures. Announcements: Hwk #1 available now, due 9/14 in class. Reading should include 1.1-1.4 of text POD? Blues? Quizzes?.

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CS 173: Discrete Mathematical Structures

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  1. CS 173:Discrete Mathematical Structures Cinda Heeren heeren@cs.uiuc.edu Rm 2213 Siebel Center Office Hours: M 4:30p, T 1:30p

  2. CS 173 Discrete Mathematical Structures Announcements: • Hwk #1 available now, due 9/14 in class. • Reading should include 1.1-1.4 of text • POD? • Blues? • Quizzes? Cs173 - Spring 2004

  3. CS 173 Discrete Mathematical Structures • Class: • Sec M: TTh 11a, 1320 DCL • Sec N: TTh 12:30p, 1310 DCL • My Office Hours: M 4:30-5:30p, T 1:30-2:30p ** • Grading: • Attendance (5%) - Starting Sept 7. • POD (10%) - Starting Sept 6 (beta testing this week). • Online weekly quiz (10%) - Starting 9/6-9/10. • Biweekly written hwk (10%) - Hwk #1 due 9/14. • Midterm exams 1 and 2 (20% each) • Final exam (25%) Cs173 - Spring 2004

  4. CS 173 Discrete Mathematical Structures • Text: Rosen • Infrared devices: (in bookstores by Thur) • Automated attendance • Class participation • Class keys: • Section M S3395Z353 • Section N W5657S385 • Register for course at www.einstruction.com • Web: www-courses.cs.uiuc.edu/~cs173 Cs173 - Spring 2004

  5. CS 173 Discrete Mathematical Games What’s That On My Head? • In each group there is at least 1 red card. • When you know your color, you get a prize. • Inquisitor repeatedly queries “do you know what’s on your head?” • How many queries until everyone knows what they have? Cs173 - Spring 2004

  6. Table entries: # of queries required to deduce # of red cards. 1 2 3 4 1 2 3 4 CS 173 Discrete Mathematical Games What’s That On My Head? # red cards 1 2 Group size 1 2 3 Cs173 - Spring 2004

  7. not both! CS 173 Propositional Logic A proposition is a declarative statement that is either TRUE or FALSE. Examples: • CS173 is Ed’s favorite class. • 3 + 2 = 5 • 3 + 2 = 32 • The Earth is flat. • The Earth is an oblate spheroid. • There is no gravity. Non-Examples: • Study hard!! • Will you meet me for coffee? • 3 + 2 • x + y = z Cs173 - Spring 2004

  8. CS 173 Propositional Logic - negation Suppose p is a proposition. The negation of p is written p and has meaning: “It is not the case that p.” • Ex. It is not the case that cs173 is Ed’s favorite class. Truth table for negation: Cs173 - Spring 2004

  9. CS 173 Propositional Logic - more operators Conjunction: p  q corresponds to English “and.” Proposition p  q is true when p and q are both true. • Ex. Maria is brave and clever. Truth table for conjunction: Cs173 - Spring 2004

  10. CS 173 Propositional Logic - more operators Disjunction: p  q corresponds to English “or.” Proposition p  q is true when p or q (or both) is true. • Ex. Maria is brave or nuts. Truth table for disjunction: T T T F Cs173 - Spring 2004

  11. CS 173 Propositional Logic - more operators Exclusive Or: p  q corresponds to English “either…or…” Proposition p  q is true when p or q (not both) is true. • Ex. You will eat either pizza or a burrito for lunch. Truth table for exclusive or: F T T F Cs173 - Spring 2004

  12. CS 173 Propositional Logic - more operators Implication: p  q corresponds to English “if…then…” • Ex. If it is raining, then it is cloudy. • Ex. If there are 200 students in the room then I am the Easter Bunny. • Ex. If p then 2 + 2 = 4. (always true…why?) Truth table for implication: T F T T Cs173 - Spring 2004

  13. CS 173 Propositional Logic - more operators Biconditional: p  q corresponds to English “if and only if…then…” • Ex. If and only if it is raining, then it is cloudy. • Ex. If and only if there are 200 students in the room then I am the Easter Bunny. Truth table for biconditional: T F F T Cs173 - Spring 2004

  14. 16 CS 173 Propositional Logic - more operators? • How many of these could we do? • How many of them do we need? To answer, we need a notion of “logical equivalence.” If p and q are propositions, then p q if their truth tables are the same. If p q, we say “p is equivalent to q.” Cs173 - Spring 2004

  15. CS 173 Propositional Logic - logical equivalence • Ex. p  q  p  q Cs173 - Spring 2004

  16. CS 173 Propositional Logic - special definitions • Contrapositives: p  q and q  p Ex. “If it is noon, then I am hungry.” “If I am not hungry, then it is not noon.” • Converses: p  q and q  p Ex.“If it is noon, then I am hungry.” “If I am hungry, then it is noon.” • Inverses: p  q and p  q Ex.“If it is noon, then I am hungry.” “If it is not noon, then I am not hungry.” Cs173 - Spring 2004

  17. YES NO NO CS 173 Propositional Logic - special  • Contrapositives: p  q  q  p ? Ex. “If it is noon, then I am hungry.” “If I am not hungry, then it is not noon.” • Converses: p  q  q  p ? Ex.“If it is noon, then I am hungry.” “If I am not hungry, then it is not noon.” • Inverses: p  q  p  q ? Ex.“If it is noon, then I am hungry.” “If it is not noon, then I am not hungry.” Cs173 - Spring 2004

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