Deductive Reasoning

Deductive Reasoning (G.1d)Obj: SWBAT apply the laws of validity: Detachment, Contrapositive & Syllogism and the symbolic form (2.4).Homework (day 20)Validity worksheet/1st NW packet complete/Quiz next blockStudy for 1st Nine Weeks Test-(prior tests/quizzes/Sol questions from binder)Storybook grade: Logic and 1st NW ReflectionPearson due Friday/Online Extra Credit will close on Oct 31st Warm-Up: Day 17 worksheet, illustrate the given statements in the form of Venn Diagrams; 1st NW packet**hw/hw log/storybook: Logic/Nine Weeks packetExtra Credit- 1st NWSince the VA Benchmark was not loading, I have substituted NATIONAL Benchmark 2 in lieu of the VA benchmark. This will close on Oct 31If you would like me to enter it, after you take it, give me a piece of paper with your: name, block and tell me you want me to record it into HAC as a quiz grade.Let p = a dog eats breadLet q = the dog gains weightLet r = the dog gets fat

1) p q, If a dog eats bread, then the dog gains weight is a true statement. Johns dog eats bread. What can be concluded? Justify. Johns dog gains weight. Law of Detachment.

2) p q means If a dog eats bread, then the dog gains weight. p q is a true statement.State the contrapositive. Is it a true statement?If the dog does not gain weight, then the dog does not eat bread is a true statement.

3) p q means If a dog eats bread, then the dog gains weight.q r means If the dog gains weight, then the dog gets fat.Using the law of syllogism, what is the logical conclusion?If a dog eats bread, then the dog gets fat.

Copy into SOL Binder (G.1)- day 20

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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. We have a Kia.

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.

Law of ContrapositiveLaw of Contrapositive: If p q is true and q is not true, then p is not true.Symbolic Representation: p q ~q ~pEx: If you do your home work, then you will passthis class. Shane did not pass the class.Shane did not do his homework

Law of DetachmentLaw 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 qp

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

Law of SyllogismLaw 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 qq r

Ex: The sun is a star. Stars are in constant motion. The sun is in constant motion. The sun is in constant motion