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Deductive Reasoning (G1d,e,ef)

Deductive Reasoning (G1d,e,ef). Obj : SWBAT apply the laws of validity: Detachment, Contrapositive & Syllogism and the symbolic form. Warm-Up: Nine Weeks Review packet ** hw / hw log/storybook: “Logic”/Nine Weeks packet. Homework (day 20)

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Deductive Reasoning (G1d,e,ef)

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  1. Deductive Reasoning (G1d,e,ef) Obj: SWBAT apply the laws of validity: Detachment, Contrapositive & Syllogism and the symbolic form. Warm-Up: Nine Weeks Review packet **hw/hw log/storybook: “Logic”/Nine Weeks packet Homework (day 20) Storybook grade: “Logic” and your “”First Nine Weeks Goal” page First Nine Weeks TEST next block- graph paper & compass Yankee Candle Money due Oct 31st Pearson due Friday Online Extra Credit will close on November 1st

  2. Deductive reasoning- Facts & definitions, accepted proportions and the laws of logic to form a logical argument. Determine if the statements are valid or invalid. Justify. 1. In-line skaters live dangerously. If you live dangerously, then you like to dance. If you are an in – line skater, then you like to dance. 2. If you drive safely, the life you save may be your own. The life Casey saves may not be her own. She does not drive safely. 3. If a figure is a rectangle, then its opposite sides are congruent. AB  DC and AD  BC. ABCD is a rectangle.

  3. Determine what, if anything can be concluded. Justify. 1. If two angles are vertical, then they do not form a linear pair. If two angles are vertical, then they are congruent. 2. If you eat to live, then you live to eat. Paula does not live to eat. 3. Cars are useful. Useful cars are practical.

  4. Law of Contrapositive Law of Contrapositive: If p → q is true and q is not true, then p is not true. Symbolic Representation: p → q ~q ~p Ex: If you do your home work, then you will pass this class. Shane did not pass the class. Shane did not do his homework

  5. Law of Detachment Law of Detachment- If the Hypothesis of a conditional statement is true, then the conclusion is also true. If p → q is true and p is true, then q is true. Symbolically: p → q p Ex: • Angles that are supplementary have measures with a sum of 180°. < A and < B are Supplementary < A and < B measures are a sum of 180°

  6. Law of Syllogism Law of Syllogism: If hypothesis p, then conclusion q. If hypothesis q , then conclusion r. (if both above statements are true) If hypothesis p, then conclusion r. (Then the above is also true) Symbolically: p → q q → r Ex: • The sun is a star. Stars are in constant motion. The sun is in constant motion. The sun is in constant motion

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