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Unformatted text preview: 1 CMSC 250 Discrete Structures CMSC 250 Lecture 1 January 2428, 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....
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