2.3 Deductive Reasoning

2.3 Deductive Reasoning - 2. It is raining. What follows?...

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2.3 Deductive Reasoning 2.3 Deductive Reasoning p. 87
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Reminders Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p q q → p ~p → ~q ~q → ~p p ↔ q
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Ex : Given: p – it is 4 th period q – it is time for lunch Write p→q. If it is 4 th period, then it is time for lunch. Write ~p. It is not 4 th period. Write p↔q. It is 4 th period iff it is time for lunch. Is p↔q true?
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Laws of Deductive Reasoning Laws of Deductive Reasoning 1. Law of Detachment 2. Law of Syllogism
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Law of Detachment Law of Detachment If a statement p→q is given and a second statement p is given, then a third statement q results. Given: p→q p q Ex: 1. If x is even, then x 2 is even. 2. x = 6 What statement follows? 6 2 is even p p q
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More examples Given : 1. If it is raining, then the ground is wet.
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Unformatted text preview: 2. It is raining. What follows? The ground is wet. Given : 1. If an < is between 0 o and 90 o , then it is acute. 2. <B is acute. What follows? No conclusion. p p q p q q Law of Syllogism Law of Syllogism If pq is given and qr is given, then pr results. Given: pq qr pr Example Example : Given: 1. If Tony is sick on Friday, then he cannot play football. 2. If Tony cannot play football, then the team will lose. What statement follows? If Tony is sick on Friday, then the team will lose. p p q q r r p q q r p r Example Example : Given : pq qs rs rq What follows? No conclusion. Given : qr st rs pq What follows? pt Assignment Assignment...
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2.3 Deductive Reasoning - 2. It is raining. What follows?...

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