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/1 st NW packet complete/Quiz next block Study for 1 st Nine Weeks Test- (prior tests/quizzes/Sol questions from binder) Storybook grade: “Logic” and 1 st NW Reflection Pearson due Friday/Online Extra Credit will close on Oct 31 st Warm-Up: Day 17 worksheet, illustrate the “given” statements in the form of Venn Diagrams; 1 st NW packet **hw/hw log/storybook: “Logic”/Nine Weeks packet

Extra Credit- 1 st NW Since the VA Benchmark was not loading, I have substituted NATIONAL Benchmark 2 in lieu of the VA benchmark. This will close on Oct 31 If 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 bread”Let q = “the dog gains weight” Let r = “the dog gets fat” 1) p → q, “If a dog eats bread, then the dog gains weight” is a true statement. John’s dog eats bread. What can be concluded? Justify. John’s 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

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 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

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°

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