The Lost Art of Argument Logic The Lost Art of Argument

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

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?

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

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

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

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

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

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

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

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?

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

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