CK12 - Geometry

Inductivereasoningmeansreasoningfrom examples.You may look at a few examples,or many. Enough
examplesmightmakeyoususpectthat a relationshipis true always,or mightevenmakeyousureof this.
But until you go beyondthe inductivestage,you can’tbe absolutelysure that it is alwaystrue.

That’s wheredeductivereasoningentersand takesover. We havea suggestionarrivedat inductively. We
then applyrulesof logic to prove,beyondany doubt,that the relationshipis true always.We will use thelaw
of detachmentand thelaw of syllogism,and otherlogic rules,to buildtheseproofs.

SymbolicNotationand Truth Tables

Logichas its own rulesand symbols.We havealreadyusedletterslike and to representstatements:
for the negation(“not”),and the arrow to indicateif-then.Hereare two moresymbolswe can use.

= and

= or

Truth tablesare a way to analyzestatementsin logic.Let’s look at a few simpletruth tables.

Example 1

How is relatedto logically?We makea truth tableto find out. Beginwith all the possibletruth values

of. This is very simple; can be eithertrue (T), or false(F).

T

F

Nextwe writethe correspondingtruth valuesfor has the oppositetruth valueas. If is true,

then is false,and vice versa.Completethe truth tableby fillingin the column.

T F

F T

Now we constructtruth tablesfor slightlymorecomplexlogic.

Example 2

Drawa truth tablefor and written.

Beginby fillingin all the T/F combinationspossiblefor and.

T T

T F

F T

F F