2.3 Deductive Reasoning

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

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
2.3 Deductive Reasoning 2.3 Deductive Reasoning p. 87
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Reminders Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p q q → p ~p → ~q ~q → ~p p ↔ q
Background image of page 2
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?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Laws of Deductive Reasoning Laws of Deductive Reasoning 1. Law of Detachment 2. Law of Syllogism
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
More examples Given : 1. If it is raining, then the ground is wet.
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

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 p→q is given and q→r is given, then p→r results. • Given: p→q q→r p→r 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 : p→q q→s r→s r→q What follows? No conclusion. • Given : q→r s→t r→s p→q What follows? p→t Assignment Assignment...
View Full Document

This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

Page1 / 10

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

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online