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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Do Now: Aim: What is the conjunction and disjunction of the truth? True or False Math is a 4-letter word and 4 th period starts at 10:25 am. George Washington was the first president of the United States and John Lennon is alive. T F

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Compound Statement A compound statement is formed by combining simple statements with one or more operators. “and” is and operator and is represented symbolically as ˄ Conjunction Math is a 4-letter word and 4th period starts at 10:25 am. T George Washington was the first president of the United States and John Lennon is alive. F

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Conjunction - Symbolically Let p represent the simple statement “The earth is a spherical ball.” Let q represent the simple statement “The earth is the third planet in our solar system.” T T The earth is a spherical ball and the earth is the third planet in our solar system. p ˄ q T

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Symbolic Let p represent the simple statement “Kobe Bryant is a basketball player.” Let q represent the simple statement “Derek Jeter is a basketball player.” T F Kobe Bryant is a basketball player and Derek Jeter is a basketball player. p ˄ q F

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Evaluating the Truth Let p represent the simple statement “The Mets are a baseball team based in Los Angeles.” Let q represent the simple statement “The Jets are a football team based in Chicago.” F F The Mets are a baseball team based in Los Angeles and The Jets are a football team based in Chicago. p ˄ q F

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Truth Table - Conjunction pq p ˄ q TTT TFF FTF FFF If p and q represent simple statements then the truth table for compound statements with the ‘and’ operator (Conjunction) is

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Evaluating the Truth Let p represent “Staten Island is a borough of NYC.” Let q represent “SI is connected to Brooklyn via the Verrazano Bridge.” Let r represent “SI has a greater population than Brooklyn.” T T F What is the truth value of the following? a) p ˄ rb) p ˄ ~r c) ~p ˄ ~rd) p ˄ q ˄ ~r

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Model Problem pq T T F F T F T F T F F T T F F F T F T T Construct the truth table for the following: ~( ~p ˄ q ) ~p ~p ˄ q ~(~p ˄ q)

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Disjunction “or” is and operator and is represented symbolically as ˅ Disjunction A compound statement is formed by combining simple statements with one or more operators. Home plate is 60’ 6” from the pitching mound or a football field is 100 yards long. First base is 90 feet from home plate or a football field is 100 feet long. The Petrides school is located in Brooklyn or October follows November in the calender year. T T F

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Truth Table - Disjunction pq p ˅ q TTT TFT FTT FFF If p and q represent simple statements then the truth table for compound statements with the ‘or’ operator (Disjunction) is

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Symbols Words Let m represent “The grass is green.” Let n represent “The hit was a single.” Let s represent “The first baseman made the out.” Rewrite: a) m ˅ n b) ~n ˅ s c) ~n ˅ ~s The grass is green or the hit was a single. The hit was not a single or the first baseman made the out. The hit was not a single or the first baseman did not make the out.

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Order of Operations Parentheses indicate order of operations. ~(n ˄ m)? negation of the statement ‘n and m” Ex. n is a true statement and c is a false statement. What is the truth value of the compound statement (n ˅ c) ˄ ~(n ˄ c) (T ˅ F) ˄ ~(T ˄ F) T ˄ ~(F) T ˄ T T

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Model Problem Construct a truth table for the following compound statement: ~(p ˄ q) ˄ [(p ˅ q) ˄ q] pq T T F F T F T F p ˄ qp ˄ q T F F F F T T T T T T F T F T F F F T F ~(p ˄ q)p ˅ q [(p ˅ q) ˄ q] ~(p ˄ q) ˄ [(p ˅ q) ˄ q]

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Aim: Logic – Conjunction/Disjunction Course: Math Lit. Model Problem Suppose p is T and q if F. Find the truth values for the following statements. Let p: I eat spinach.q: I am strong. a)~(p ˄ q) b)~p ˄ q

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رياضيات متقطعة لعلوم الحاسب MATH 226. Text books: (Discrete Mathematics and its applications) Kenneth H. Rosen, seventh Edition, 2012, McGraw- Hill.

رياضيات متقطعة لعلوم الحاسب MATH 226. Text books: (Discrete Mathematics and its applications) Kenneth H. Rosen, seventh Edition, 2012, McGraw- Hill.

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