DeductiveReasoning
LearningObjectives
- Recognizeand applysomebasicrulesof logic.
- Understandthe differentpartsthat inductivereasoningand deductivereasoningplay in logicalreasoning.
- Use truth tablesto analyzepatternsof reasoning.
Introduction
You beganto studydeductivereasoning,orlogic,in the last section,whenyou learnedaboutif-thenstate-
ments.Now we will see that logic,like otherfieldsof knowledge,has its own rules.Whenwe followthose
rules,we will expandour baseof factsand relationshipsaboutpoints,lines,and planes.We will learntwo
of the mostusefulrulesof logic in this section.
DirectReasoning
We all use logic—whetherwe call it that or not—inour dailylives.And as adultswe use logicin our work
as well as in makingthe manydecisionsa personmakeseveryday.
- Whichproductshouldyou buy?
- Who shouldyou vote for?
- Will this steelbeamsupportthe weightyou placeon it?
- Whatwill be your company’s profitnext year?
Let’s see how commonsenseleadsto the two mostbasicrulesof logic.
Example 1
SupposeBea makesthe followingstatements,whichare knownto be true.If CentralHigh Schoolwins today, they will go to the regionaltournament.CentralHigh Schooldoeswin today.Commonsensetells us that thereis an obviouslogicalconclusionif thesetwo statementare true:CentralHigh Schoolwill go to the regionaltournament.Example 2
Hereare two true statements.is an odd number.Everyodd numberis thesumof an evenand an odd number.Basedon only thesetwo true statements,thereis an obviousfurtherconclusion:is the sum of an evenand an odd number.(this is true, since ).