离散数学(二)

《离散数学(二)》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、DiscreteMathematicsShandongUniversitySoftwareCollege8/14/2021Chapter5Relations8/14/2021Relations/Relationshop?Thinkoverthepropertyofsomerelations?Schoolmate同学Paternity父子Sibling妹兄弟friendsrelationship朋友Roommate舍友Romanticrelationship恋人Soon.8/14/2021§5.1Relationsandth

2、eirproperties(1)5.1.1TheconceptofrelationDefinition：LetAandBbesets.AbinaryrelationfromAtoBisasubsetofAB.8/14/2021§5.1Relationsandtheirproperties(1)5.1.2Functionasrelations8/14/2021§5.1Relationsandtheirproperties(2)5.1.3RelationonasetDefinition：ArelationonthesetAis

3、arelationfromAtoA.8/14/2021§5.1Relationsandtheirproperties(3)5.1.4Propertiesofrelations（1）ReflexiveandIrreflexiveDefinition：ArelationRonasetAiscalledreflexiveif(a,a)RforeveryelementaA.ArelationRonasetAisirreflexiveif(a,a)RforallaA.8/14/2021§5.1Relationsandtheir

4、properties(4)5.1.4Propertiesofrelations（2）SymmetricandAntisymmetricDefinition：ArelationRonasetAiscalledsymmetricif(b,a)Rwhenever(a,b)R,foralla,bA.8/14/2021§5.1Relationsandtheirproperties(5)5.1.4Propertiesofrelations（2）SymmetricandAntisymmetricDefinition：Arelatio

5、nRonasetAsuchthat(a,b)Rand(b,a)Ronlyifa=b,foralla,bA,iscalledantisymmetric.8/14/2021§5.1Relationsandtheirproperties(6)5.1.4Propertiesofrelations（3）TransitiveDefinition：ArelationRonasetAcalledtransitiveifwhenever(a,b)Rand(b,c)R,then(a,c)R,foralla,b,cA.8/14/20

6、21特殊关系自反性反自反性对称性反对称性传递性空关系ⅹ√√√√全域关系EA√ⅹ√ⅹ√恒等关系IA√ⅹ√√√P(A)上的包含关系√ⅹⅹ√√三角形的相似关系√ⅹ√ⅹ√§5.1Relationsandtheirproperties(7)5.1.4Propertiesofrelations8/14/2021§5.1Relationsandtheirproperties(7)5.1.5CombiningrelationsDefinition：LetRbearelationfromasetAtoasetBandSarelationfro

7、mBtoasetC.ThecompositeofRandSistherelationconsistingoforderedpairs(a,c),whereaA,cC,andforwhichthereexistsanelementbB,suchthat(a,b)Rand(b,c)S.WedenotethecompositeofRandSbySR.8/14/2021§5.1Relationsandtheirproperties(7)5.1.5InverserelationsDefinition：LetRbearela

8、tionfromasetAtoasetB.TheInverserelationofRistherelationconsistingoforderedpairs(b,a),whereaA,bB,andforwhichthereexists(a,b)R.WedenotetheInvers