Download Geometry 2.3 ‐ Deductive Reasoning A. Deductive Reasoning ‐ a

Geometry
2.3 ‐ Deductive Reasoning
A. Deductive Reasoning ‐ a system of reasoning used to reach logical conclusions from given statements
• Two Laws of Deductive Reasoning
B. The Law of Detachment:
• If p → q is a true conditional, and p’ is true, then q’ is true
• Whenever you have a conditional that is true and you are given another hypothesis that satisfies the hypothesis of the original conditional, then you can make a conclusion
EXAMPLE: If I score a TD, then my team earns 6 points. Willie scored a TD, then _______________.
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C. Examples of the Law of Detachment. Use the Law of Detachment to draw a conclusion. If no conclusion can be drawn, say “no conclusion.”
1. If you like walking, then you’ll love NIKE AirWalk shoes.
Kelly likes walking.
2. If x and y are both negative, then x times y is positive.
x = ‐3 and y = ‐5
NOTE: If you have a conditional that is true and you are given a conclusion that satisfies the conclusion of the original conditional, a conclusion cannot be drawn
3. If you like walking, then you’ll love NIKE AirWalk shoes.
Eric loves NIKE AirWalk shoes.
4. If x and y are both negative, then x times y is positive.
x(y) = 20
5. If a vehicle is a car, then it has four wheels.
A sedan is a car.
6. If you want a steak that’s grilled to perfection, then go to Morton’s.
Gail went to Morton’s.
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D. The Law of Syllogism:
• If p → q and q → r are true conditionals, then p → r follows as a true conditional.
E.
Examples. Use the Law of Syllogism to draw a conclusion if possible. 1.
I am taller than Sally and Sally is taller than Jane. Conclusion?
2. If a metal is liquid at room temperature, then it is mercury. If a metal is mercury then its chemical symbol is Hg. Conclusion?
3. If Anna takes the car to the store, then she will stop at the post office. If Anna stops at the post office, then she’ll buy stamps. Conclusion?
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F. Use either Law to reach a conclusion. If a conclusion exists, state which law was used. 1. If you want the best hamburger in town, then buy a Biggie Burger
Pat bought a Biggie Burger
2. If is a segment, then AB≅ AB
AB
CD is a segment
3. If two angles form a linear pair, then they share a common ray
If two angles share a common ray then they are adjacent
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2.3 HW p. 96 #s 1 ­ 14, don't do #4
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