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Direct Proof

Direct Proof. Section 2.3. Syllogism :. Law of Logic Greek: “sy” from “syn” (means the same) “logos” (means reasoning) Argument in the form: a  b b  c a  c (therefore) (note: similar to transitive property). Syllogism: (Euler diagrams).

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Direct Proof

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  1. Direct Proof Section 2.3

  2. Syllogism: • Law of Logic • Greek: “sy” from “syn” (means the same) “logos” (means reasoning) • Argument in the form: a  b b  c a  c (therefore) (note: similar to transitive property)

  3. Syllogism: (Euler diagrams) a  b b  c a  c Extend pattern ---- Rube Goldberg: a  b b  c c  d d  e a  e b c c b a b a

  4. Direct Proof: • premises: statements of the argument • conclusion: connects the first to the last Note: If all premises are true and the logic of the argument is correct, then the conclusion must be true. • theorem: a statement that is proved by reasoning deductively from already accepted statements (review: deductive reasoning - use of logic to draw conclusions from statements already accepted as true)

  5. Using syllogism write the conclusion statement, if possible: 1) If a number is a whole number, then it is an integer. If a number is an integer, then it is a rational number. If a number is a whole number, then it is a rational number. 2) If x = 2 then 6x = 12. If 6x = 12 then 3x = 6. If x = 2, then 3x = 6.

  6. Hint: Always rewrite statements in “if - then” format first!!! 3) If a figure is a rectangle, then it has four sides. A figure is a quadrilateral if it has four sides. (If is has four sides, then it is a quadrilateral.) If a figure is a rectangle, then it is a quadrilateral. 4) I will not do my homework if I watch TV. Mrs. Marieni will be disappointed if I do not do my homework. (If I watch TV, then I will not do my homework.) (If I do not do my hw, then Mrs. Marieni will be disappointed.) If I watch TV, then Mrs. Marieni will be disappointed.

  7. Homework: • Read p 50-51 • Do p 52 #1 – 32 (a lot of writing!)

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