Document Sample

Statements and negations (3.1) p. 88-93 Compound statements and connectives (3.2) p. 94-101 OBJECTIVES: Express statements using symbols Form the negation of statements Form compound statements using connectives Statements – a sentence that is either true or false, but not both simultaneously, p. 89 Examples 5<9 17 < 9 11 > 5 All two digit numbers are greater than 1 digit numbers Negation- a statement with an opposite “truth. When a statement is true its negation is false and when the statement is false its negation is true. p. 89 Statements - “Symbolism” Just as x can be used as a name for a number, a symbol such as p can be used as a name for a statement. When p is used as a name for a statement the symbols ~p are used as a name for the negation of p. Examples Let p stand for “Miami is a city in Florida.” Then ~p is the statement “Miami is not a city in Florida.” “Quantified” Statements A “quantified” statement is one that says something about “all”, “some”, or “none” of the objects in a collection. Examples “All students in the college are taking history.” “Some students are taking mathematics.” “No students are taking both mathematics and history.” “Equivalent” Statements In any language there are many ways to say the same thing. The different linguistic constructions of a statement are considered equivalent. Example “All students in the college are taking history.” “Every student in the college is taking history.” Example “Some students are taking mathematics.” “At least one student is taking mathematics.” Negating Quantified Statements The negation of a statement about “all” objects is “not all”. “Not all” can often be expressed by “some are not.” Examples p : All students in the college are taking history. ~p : Some students in the college are not taking history. Negating Quantified Statements The negation of a statement about “some” objects is “not some”. “Not some” can often be expressed by “none” or “not any.” Examples p : Some students are taking mathematics. ~p : None of the students are taking mathematics. “Compound” Statements, 94 Simple statements can be connected with “and”, “Either … or”, “If … then”, or “if and only if.” These more complicated statements are called “compound.” Examples “Miami is a city in Florida” is a true statement. “Atlanta is a city in Florida” is a false statement. “Either Miami is a city in Florida or Atlanta is a city in Florida” is a compound statement that is true. “Miami is a city in Florida and Atlanta is a city in Florida” is a compound statement that is false. “And” Statements, p. 95 When two statements are represented by p and q the compound “and” statement is p /\ q. p: Harvard is a college. q: Disney World is a college. p/\q: Harvard is a college and Disney World is a college. p/\~q: Harvard is a college and Disney World is not a college. “Either ... or” Statements, p. 96 When two statements are represented by p and q the compound “Either ... or” statement is p\/q. p: The bill receives majority approval. q: The bill becomes a law. p\/q: The bill receives majority approval or the bill becomes a law. p\/ ~q: The bill receives majority approval or the bill does not become a law. “If ... then” Statements, p. 96 When two statements are represented by p and q the compound “If ... then” statement is: p q. p: Ed is a poet. q: Ed is a writer. p q: If Ed is a poet, then Ed is a writer. q p: If Ed is a writer, then Ed is a poet. ~q ~p: If Ed is not a writer, then Ed is not a Poet “If and only if” Statements, p.98 When two statements are represented by p and q the compound “if and only if” statement is: p q. p: The word is set. q: The word has 464 meanings. p q: The word is set if and only if the word has 464 meanings. ~q ~p: The word does not have 464 meanings if and only if the word is not set. Symbolic Logic, p. 99 Statements of Logic Name Symbolic Form Negation ~p Conjunction p/\q Disjunction p\/q Conditional pq Biconditional p q “Truth Tables” – Negation, p. 103 If a statement is true then its negation is false. If the statement is false then its negation is true. This can be represented in the form of a table called a “truth table.” p ~p T F F T “Truth Tables” – Conjunction, p.104 The conjunction of two statements is true only when both of them are true. p q pq T T T T F F F T F F F F “Truth Tables” – Disjunction, p.106 The disjunction of two statements is false only when both of them are false. p q pq T T T T F T F T T F F F Constructing a Truth Table, p. 107 Construct a truth table for ((p/\~q)\/q). p q ~q (p~ q) (p~ q)q T T F F T T F T T T F T F F T F F T F F HOMEWORK Officehours M-F 9:00-10:15 Beach Bldg Room 113 or by appointment Work p.93 #1-30 odd Work p.101 Read p. 103-123 (3.3, 3.4) PRE QUIZ

DOCUMENT INFO

Shared By:

Categories:

Tags:
Statements, negations, (3.1), 88-93, Compound, statements

Stats:

views: | 43 |

posted: | 4/8/2009 |

language: | English |

pages: | 18 |

OTHER DOCS BY cantaloop

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.