128 CHAPTER8. CONTROLSTRUCTURES,PART 2

P Q PandQ

T T T

T F F

F T F

F F F

Inthistable,PandQrepresentsmallerBooleanexpressions.Sinceeachexpressionhastwo possiblevalues,
therearefourpossiblecombinationsofvalues,eachshownasonerow inthetable.Thelastcolumngivesthe
valueofPandQforeachpossiblecombination.Bydefinition,theandis trueonlyinthecasewhereboth
PandQaretrue.
Theoroftwo expressionsis truewheneitherexpressionis true.Hereis thetruthtabledefining or:

P Q PorQ

T T T

T F T

F T T

F F F

Theonlytimetheoris falseis whenbothexpressionsarefalse.Noticeespeciallythatoris truewhenboth
expressionsaretrue.Thisis themathematicaldefinitionofor, buttheword“or”is sometimesusedinan
exclusive senseineverydayEnglish.If yourmomsaidthatyoucouldhave cake orcookiesfordessert,she
wouldprobablyscoldyoufortakingboth.
Thenotoperatorcomputestheoppositeofa Booleanexpression.It is aunaryoperator, meaningthatit
operatesona singleexpression.Thetruthtableis verysimple.

P notP

T F

F T

UsingBooleanoperators,it is possibletobuildarbitrarilycomplex Booleanexpressions.Aswitharith-
meticoperators,theexactmeaningofa complex expressiondependsontheprecedencerulesfortheoperators.
Considerthisexpression.

a or not b and c

How shouldthisbeevaluated?
Pythonfollowsa standardconventionthattheorderofprecedenceisnot, followedbyand, followedby
or. Sotheexpressionwouldbeequivalenttothisparenthesizedversion.

(a or ((not b) and c))

Unlike arithmetic,however, mostpeopledon’t tendtoknow orremembertheprecedencerulesforBooleans.
I suggestthatyoualwaysparenthesizeyourcomplex expressionstopreventconfusion.
Nowthatwehave someBooleanoperators,wearereadytoreturntoourexampleproblem.To testfor
theco-locationoftwo points,wecoulduseanandoperation.

if p1.getX() == p2.getX()and p2.getY() == p1.getY():

points are the same

else:

points are different

Heretheentireexpressionwillonlybetruewhenbothofthesimpleconditionsaretrue.Thisensuresthat
boththexandycoordinateshave tomatchforthepointstobethesame.Obviously, thisis muchsimplerand
clearerthanthenestedifs fromthepreviousversion.
Let’s lookat a slightlymorecomplex example.Inthenextchapter, wewilldevelopa simulationforthe
gameofracquetball.Partofthesimulationwillneedtodeterminewhena gamehasended. Supposethat
scoreAandscoreBrepresentthescoresoftwo racquetballplayers.Thegameis overassoonaseitherof
theplayershasreached 15 points.Hereis a Booleanexpressionthatis truewhenthegameis over: