1 / 12

L 2 Chapter 1

L 2 Chapter 1. Logic and Proofs. Topics. Logic Proposition Compound proposition Conjunction (AND) Dis conjunction (OR) And TRUE Table Or TRUE Table Not TRUE Table. Logic. The study of reasoning Concerned with whether reasoning is correct or not.

karli
Download Presentation

L 2 Chapter 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. L 2 Chapter 1 Logic and Proofs

  2. Topics • Logic • Proposition • Compound proposition • Conjunction (AND) • Dis conjunction (OR) • And TRUE Table • Or TRUE Table • Not TRUE Table

  3. Logic • The study of reasoning • Concerned with whether reasoning is correct or not. • Focuses on relationship as opposed to content of any particular statement. • Logic is used in math to prove Thermo. • Logic is used in computer programs to prove if a program does what it supposed to do.

  4. Logic • When logic is used in math, a general method of proof is used called math induction. • Used throughout math and computer Science specially in discrete math.

  5. Proposition (p) • A statement that is either True or False but not both. • Examples: • The Class starts at 12:00 • Jackie is over than 22 years old. • We will use p, q, r to perform propositions

  6. Proposition • Proposition is a declarative statement not an order or a command. • Joe is single  a proposition • Is Joe single?  NOT a proposition • Are you single?  NOT a proposition. • Do you homework. NOT a proposition • P: 1 + 4 = 10 T or F • P: it is cold T or F • q: it is raining T or F

  7. Compound Proposition • In ordinary speeches we use the words AND & OR • p AND q is denoted as p ^ q • p or q is denoted as p v q Proposition resulted from combining the above propositions is called compound proposition.

  8. Compound position • P: It is Cold and Raining (Cold ^ Raining) • Possibilities: • Cold and also Raining • Cold but not Raining • Not Cold but Raining • Not Cold and Not Raining • Same logic and similar propositions for (OR V) • P: It is Cold or Raining (Cold V Raining)

  9. Conjunction and Disconjunction • Conjunction: • p and q • p && q • p ^ q • Disconjunction: • p or q • p || q • p V q

  10. Negation (Not) • Denoted by the symbol ¬ • NOT p • ¬ p • ¬ q

  11. The truth table for the compound proposition p^ q And truth p ^ q True is denoted by 1 and False is denoted by 0 If P: 5 + 6 = 10 q =7 Then p ^ q is F

  12. The truth table for the compound proposition pV q And truth p V q True is denoted by 1 and False is denoted by 0 If P: 5 + 6 = 10 q =7 Then p V q is T

More Related