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Unformatted text preview: CPSC 121 Lecture 11 January 28, 2009 Menu January 28, 2009 Topics: Predicates and Quantified Statements (cont’d) Reading: Today: Epp 2.2–2.4 Reminders: Assignment 1 due Friday, January 30, 17:00 In-class Quiz 1 Wednesday, February 4 Midterm exam Tuesday, February 24 (evening) READ the WebCT Vista course announcements board As noted above, Assignment 1 is due Friday, January 30, 17:00. Here is further information from the “Assignments, Labs, Online Quizzes” section of the course web site . The hand-in boxes for CPSC 121 are in the basement of the ICCS building and are labeled with the course number, section number and instructor’s name. They are in the hallway outside of room 011. Assignment submissions must be stapled below the CPSC 121 assignment cover page or a clearly legible reproduction of the same information. Late submissions are not accepted. Predicates and Quantified Statements (cont’d) Lecture 9 ended with two logical equivalences... Two Important Logical Equivalences ∀ x,P ( x ) ≡ ∃ x, P ( x ) ∃ x,P ( x ) ≡ ∀ x, P ( x ) These two logical equivalences are referred to as Generalized De Morgan’s Laws NOTE: We’ve already observed that universal quantification generalizes conjunction and that existential quantification generalizes disjunction. The generalized De Morgan’s Laws also follow from this observation These two logical equivalences determine, respectively, the negation of a universally quantified statement, ∀ x,P ( x ) , and the negation of an existentially quantified statement, ∃ x,P ( x ) . Epp considers the universally quantified conditional statement, ∀ x,P ( x ) → Q ( x ) , to be an important special case....
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- Spring '08
- Logic, Modus ponens, Rule of inference, quantified statements