slides01 - 1 CMSC 250 Discrete Structures CMSC 250 Lecture...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 CMSC 250 Discrete Structures CMSC 250 Lecture 1 January 24-28, 2011 2 CMSC 250 Administrative Syllabus (Online) Every week (mostly): Worksheet Quiz Homework Class webpage Two midterms, as noted on the syllabus (on the class webpage) Academic integrity 3 CMSC 250 Motivation Why learn this material? Some things can be directly applied Some things are good to know Some things just teach a way of thinking and expressing yourself 4 CMSC 250 Examples Directly applied- circuits to do addition Conditionals in if statements Things which are good to know- for example that the square root of 2 cannot be stored Way of thinking- the number of primes is infinite 5 CMSC 250 Course topics Propositional logic (and circuits) Predicate calculus - quantification Elementary number theory Mathematical induction Sets Counting - combinations and probability Functions Relations Graph theory 6 CMSC 250 Chapter 1, Propositional Logic 7 CMSC 250 Statement/proposition Declarative (true or false) Symbolized by a letter Examples: Today is Monday. 5 + 2 = 7 3 * 6 > 18 The sky is blue. Why is the sky blue? Barack Obama. Two students in the class have a GPA of 3.275. The current king of France is bald. 8 CMSC 250 Other symbols and definitions for constructing compound statements Conjunction "and" is symbolized by Disjunction "or" is symbolized by Negation "not" is symbolized by ~ (or sometimes ) 9 CMSC 250 Truth table for p q p q 1 1 1 1 1 10 CMSC 250 Truth table for p q p q 1 1 1 1 1 1 1 11 CMSC 250 Truth table for p p 1 1 12 CMSC 250 Translation of English to symbolic logic statements The sky is blue. one simple (atomic) statement- assign a letter or name to it, i.e., b The sky is blue and the grass is green. one statement conjunction of two atomic statements each single statement gets a letter or name, i.e., b, g and join with ^ i.e., b ^ g The sky is blue or the sky is purple. one statement disjunction of two atomic statements each single statement gets a name, i.e., b, p and join with i.e., b p 13 CMSC 250 Translation #1 The sky is blue or purple. two statements "the sky is blue"- name this b "the sky is purple"- name this p it's still a disjunction "the sky is blue" or "the sky is purple" b p 14 CMSC 250 Translation #2 The sky is blue but not dark....
View Full Document

Page1 / 43

slides01 - 1 CMSC 250 Discrete Structures CMSC 250 Lecture...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online