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The Lost Art of Argument
Logic The Lost Art of Argument
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Propositions Definition: Proposition – A statement that is either true or false (but not both). Examples: This shirt is red √2 is irrational 1 + 1 = 5 There are more stars than grains of sand
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Propositions Definition: Proposition – A statement that is either true or false (but not both). Not Propositions: x + 2 = 17 When is Thanksgiving? Why are these not propositions?
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Propositions Definition: Conjunction – P Λ Q (“P and Q”) Example:
P = Three quarters equal one dollar Q = 8 is an even number P Λ Q = Three quarters equal one dollar and 8 is an even number
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Propositions Definition: Disjunction – P ν Q (“P or Q”) Example:
P = Three quarters equal one dollar Q = 8 is an even number P Λ Q = Three quarters equal one dollar or 8 is an even number
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Propositions Definition: Negation - ~P (Not P) Examples:
P = Three quarters equal one dollar Q = 8 is an even number ~P = It is not the case that three quarters equal one dollar or: Three quarters do not equal one dollar ~Q = It is not the case that 8 is an even number or: 8 is not an even number
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Truth Tables P Q (P Λ Q) True False
Truth tables are a way to visually organize whether a statement is true or false. This is the truth table for: P Λ Q P Q (P Λ Q) True False
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Truth Tables P Q (P ν Q) True False
Truth tables are a way to visually organize whether a statement is true or false. This is the truth table for: P ν Q P Q (P ν Q) True False
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Truth Tables Definition: Equivalent – Two propositions are equivalent when their truth values are the same. Here are two truth tables. Are the two propositions, ~(P Λ Q) and (~P v ~Q) equivalent? P Q (P Λ Q) ~(P Λ Q) T F P Q ~P ~Q (~P v ~Q) T F
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Logic Worksheet 1. Place a check next to all statements that are propositions. a. ____ The National debt of Poland is more than $30 Billion. b. ____ Where is my book? c. ____ x + 3 = 0 d. ____ Albert Einstein never wore red boots. e. ____ Horses have gills. f. ____ x^2 ≥ 0
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Logic Worksheet 2a. Construct a proposition that is false.
2b. Write the negation of the proposition. 2c. Is the negation of the false proposition true or false? 2d, Will the negation of a false proposition always be true?
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Logic Worksheet 3. Construct truth tables for ~(P V Q) and ~P ^ ~Q
Are the propositions ~(P V Q) and ~(P V Q) equivalent? Why? P Q (P V Q) ~(P V Q) T F P Q ~P ~Q ~P ^ ~Q T F
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Logic - Review Proposition – A statement that is either true or false (but not both) Conjunction – And Disjunction – Or Negation – Not Truth Tables can be used to determine Equivalence Equivalence – Two propositions have the same truth values
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