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Write the Hypothesis, the conclusion, the inverse converse and contrapositive of the following conditional statement Starter If 3 points are collinear then the slopes of any pair of them are equal

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Geometry Chapter 2 section 3 The Deductive Argument

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Conditional Statement p q Symbolic Logic Where p and q stand for two conditions Means if p then q

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Symbolic Logic condition p = we stay quiet condition q = we can stay up p q = if we stay quiet then we can stay up

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Symbolic Logic condition p = we stay quiet condition q = we can stay up ~p = we do not stay quiet ~q = we can not stay up ~ means:

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Symbolic Logic p q ………………..Statement q p ………………… ~p ~q ……………. ~q ~p……………….

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Syllogism Syllogism is also called collapsing an argument If p q and q r then p r If the Tomatoes are ripe then you must pick them. If you pick the tomatoes then thy will make a good sauce Therefore If the tomatoes are ripe they will make a good sauce

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Put the syllogism in order a.) If Clara likes the music she get tired b.) If Clara likes the music she will dance c.) If Clara dances She will get tired

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Bad Syllogism If it’s a Police Officer then it wears dark socks If I’m working then I wear dark socks If I’m working, I’m a Police Officer p q r q Therefore if p r

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Put into Symbolic Logic If a person is a communist then they have thought about politics If a person is a social studies teacher then they have thought about politics Social studies teachers are communists

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Detachment p q…… p therefore q If it’s Sunday Aunt Tessie makes mashed potatoes and gravy It’s Sunday Therefore Aunt Tessie is making mashed potatoes and gravy Make a statement, affirm the hypothesis, re-state the conclusion

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Make a detachment using the following conditional statements 1.If I eat one chip then I’ll eat the whole bag 2.If Carla hits her brother then she’ll be in trouble 3.If I study, I’ll pass that test 4.Watermelons grow on vines

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Put into Symbolic Logic If the bus drives at less than 50 mph the bomb will go off The bomb went off The bus must have slowed down below 50 mph

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Do Now! Page 88 – 91 Problems 6 – 13 & 14 – 35 odd 37, 38 & 41 – 49 all

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Lesson 2-4 Deductive Reasoning Deductive reasoning- uses facts, rules, definitions, or properties to reach logical conclusions Law of Detachment: If p.

Lesson 2-4 Deductive Reasoning Deductive reasoning- uses facts, rules, definitions, or properties to reach logical conclusions Law of Detachment: If p.

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