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