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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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