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Logic

Logic. Eric Hoffman Advanced Geometry PLHS Sept. 2007. Key Topics. Statement – any sentence that is either true of false, but not both Often represented by using a letter such as p or q Truth Value – the truth of falsity of a statement

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Logic

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  1. Logic Eric Hoffman Advanced Geometry PLHS Sept. 2007

  2. Key Topics • Statement – any sentence that is either true of false, but not both • Often represented by using a letter such as p or q • Truth Value – the truth of falsity of a statement • Negation – the negation of a statement has opposite meaning as well as opposite truth value • Ex. : p: Perry is a town in Kansas (~p) not p: Perry is not a town in Kansas

  3. Key Topics • Compound Statement – when two or more statements are joined by using the words “and” or “or” • Conjunction – compound statement formed when using the word “and” to join two or more statements • p Λ q read: p and q • Disjunction – compound statement formed when using the word “or” to join two or more statements • p V q read: p or q

  4. Key Topics • Conjunction Truth Values : for a conjunction to be true, both p and q have to be true. • Ex. : Perry is a town in Kansas and Perry is a smaller town than Topeka. p : Perry is a town in Kansas q : Perry is a smaller town than Topeka Both true so p Λ q is true.

  5. Key Topics • Conjunction Truth Values : p : Perry has a population of 50,000 people. q : Perry is a town in Kansas. q: is true, but p: is not true, so p Λ q is not true.

  6. Key Topics • Disjunction Truth Values – for a disjunction to be true either p has to be true, q has to be true, or both are true p: Triangles have three sides q: Equilateral triangles have 3 congruent sides r: Scalene triangles have 2 congruent sides What are the truth values for the following: p V q , p V r , q V r , p Λ q , q Λ r , p Λ r

  7. Key Topics • Truth Values – the negation of a statement always has the opposite truth value p: Triangles have three sides True ~ p: Triangles do not have three sides False q: Equilateral triangles have 3 congruent sides r: Scalene triangles have 2 congruent sides What are the truth values for the following: p V ~ q , ~ p V r , ~ q V r , p Λ ~ q , ~ q Λ r , p Λ ~ r

  8. Key Topics • Truth Tables – convenient way to organize truth values.

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  11. Key Topics • In Class Example : p : A rectangle has 4 congruent angles q : A rectangle is a square r : A square is a rectangle Construct the truth table for: (q V ~r) Λ (p Λ ~q)

  12. Key Topics • Homework: Pgs. 73, 74 18-44 even, 56-72 even 23 problems!!!

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