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LOGIC LAWS

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Law of Detachment p q p _______ q

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p q ~q _______ ~p Modus Tollens

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p qp q ~p~q____ q P Law of disjunctive inference

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Drawing Conclusions using the laws Given the three statements, what conclusion can be found? If Rachel joins baseball then Rachel likes to sing Rachel will join baseball or Rachel will play basketball Rachel does not like to sing

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Rewrite the sentences into symbols: B S B A ~S Try to find two statements that form a rule B S ~S You can use Modus tollens to conclude ~B You then can use ~B to form a rule with B A You can use the law of disjunctive inference to conclude A

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Try: Given: If Billy misses the Yankees game then the red sox win If the red sox win then Billy is not happy Billy is happy Prove: Billy does not miss the Yankee game Y: Billy misses the Yankee game W: Red sox win H: Billy is happy

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Y: Billy misses the Yankee game W: Red sox win H: Billy is happy Given: Y W W ~H H Using Modus tollens W ~H H Conclude ~W Therefore using Modus tollens Y W ~W Concludes ~Y So Billy does not miss the Yankee game

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HOMEWORK Pg. 79 4-18 even Pg.83 3-6 Pg. 84-85 11, 12, 15

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Section 2.5 If-Then Statements and Deductive Reasoning pg.82.

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