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69 - fl AnelementzialnA-Bif,nndanlyif T...

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Unformatted text preview: fl. AnelementzialnA-Bif,nndanlyif.__. T. Andementmiaind‘if,nndnnlyif,_. B. Theemptyaetiseeetwith_. 9. Thepawm-uetoiaaetAiu_. 1o. SetsAnndBarediqjointif,andomlyif,_. 1L Amflecflonofnnn-ptyeebaA1,Aa,....dfliea.pnrtitinnn~fa.setdif,a.ndan]}rif,_. 12. Gimm‘iandfl,theCarteaianpmductoanndB,AxH,iB__fl. 13. Given nets A1,A=,...,AmtheCn.rtesianpmtluctA1 x1123: mxdnis . 14. ThuaeanelemantnrglmeutforpmfingthetaaatXiaamhaetalasetY,ynuauppmthat andahwthntfi ' 15. TouaethehmicmethodfmprovhgthattwueefldeYueequaLyeuprmthet andthat . 15. To prove a. proposed set itleutit}r Involving set variables A, B, and (I. you suppose that and mau that . '11HfliaamtwithmelementamddiannyaetJherelafionufflandAisthnt . :15.TuuaetheelementmethndfinpravingthatasetXequaletheemptyaet,yuuprm-ethatx hal_.‘1‘adnthia,yuusuppoeethat anflycrushuwthatthlsauppoaifiunlendsto —.u—' .19.!bahuwthatauetXisnutaaubaetofaeetY, . :21. Given a. proposed set identity inmlviug set val-inhies A, B, and If}, the moat 00mm way to ahwthatthepmpmedidmtityiafalaeintoflnd . ' . When using the “algebraic“ method for profing a. set identity, it Is important to , Theaperatbnnuf+mdomafioulemalgebnuegenemfimflmoftheopemtmof and intheaetofaflatatementaformsinagiwnfinitenumberofuriablaaandthe mentioned—and inthaaetofaflsuhealsufngivennet. Ewell Showed that the folimving prop-steed “set definition“ could not actually define a set: ;E:-__ Ming’aanlutlantothehnltingpmhlemahawed thatthereisnnmmyuteralaofithmthetwfl] meeptanyalgofitthmddamletDuinputandthenfiuindimtewhethm-mmt . :11 :hanelemmtoftheaetri thesetAiansuhaetuftheaetB; -_ fin’aflmii'zedthenzefi{‘motherwrda.mryelementofAlaalaoane]I-entuffi] exactly the sameelflmenta :lainAnrmininB aismAandxiainB eiainAandzlanc-tinfl '-'=i.inutin..l1 “II“ ...
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