Setha ithiyori manje iyingxenye yezibalo. Sonke siyazi ukuthi ibizwa ngokuthi isethi noma iliphi iqoqo lezinto elihlukaniswa ngokusobala komunye nomunye, elinesici esisodwa (noma ngaphezulu) esifana. Setha izifundo zethiyori ngezakhiwo nobudlelwano bamasethi; Le nsimu yaphakanyiswa nguBolzano noCantor, base bepheleliswa vele ngekhulu lama-20 ngezinye izibalo, njengoZermelo noFraenkel.
Kubalulekile ukuthi isethi ngayinye ichazwe ngokuphelele, okungukuthi, ukuthi ingasungulwa ngokunemba noma ngabe inikezwe into, ingeyesethi noma cha.
- Vuliwe izibalo lokhu ngokuvamile kuqondile. Isibonelo, uma iqoqo lezinombolo ezinkulu kune-1 nangaphansi kuka-15 licatshangelwa, kuyacaca ukuthi leli sethi lizokwakhiwa ngamadijithi 2, 4, 6, 8, 10, 12 no-14 kuphela.
- Ngo- ulimi oluvamile, ukukhuluma ngeqembu kungacacisa kakhulu, ngoba uma sifuna ukwakha iqembu labahlabeleli abahamba phambili, ngokwesibonelo, imibono izohluka futhi ngeke kube nokuvumelana okuphelele ngokuthi ngubani ozoba yingxenye yaleli qembu nokuthi ngubani ongeke . Amanye amasethi akhethekile amasethi angenalutho (angenawo ama-elementi) noma amasethi wokuhlangana (anento eyodwa kuphela).
I- izinto eziyingxenye yesethi zibizwa ngokuthi amalungu noma izinto, namasethi amelwe emibhalweni ebhaliwe efakwe kuma-brace: {}. Ngaphakathi kubakaki, izinto zihlukaniswa ngamakhoma. Zingamelwa futhi yimidwebo kaVenn, efaka ukuqoqwa kwezinto ezakha isethi ngayinye kulayini oqinile futhi ovalekile, imile ngendlela eyindilinga. Lapho kunemigqa eminingana yale migqa evaliwe, ngayinye inikezwa uhlamvu olukhulu (A, B, C, njll.) Futhi isethi yomhlaba wonke yalezi zimelwe uhlamvu U, okusho ukuthi isethi yomhlaba wonke.
Ngamasethi ongawenza imisebenzi; okusemqoka inyunyana, impambana-mgwaqo, umehluko, umphelelisi nomkhiqizo waseCartesian. Ukuhlanganiswa kwamasethi amabili A no-B kuchazwa njengesethi A ∪ B futhi lokhu kuqukethe into ngayinye okungenani eyodwa yazo. I-equation ejwayelekile emele lokhu:
- TO= {UJosé, uJerónimo}, B= {UMaría, uMabel, uMarcela}; AUB= {UJosé, uJerónimo, uMaría, uMabel, uMarcela}
- P= {eliphakathi, i-apula}, C= {ulamula, iwolintshi}; F= {i-cherry, i-currant};PUCUF = {eliphakathi, i-apula, ulamula, iwolintshi, i-cherry, i-currant}
- UM={7, 9, 11}, N={4, 6, 8}; UMUNTU={7, 9, 11, 4, 6, 8}
- R= {ibhola, isikeyiti, isigwedlo}, G= {gwedla, ibhola, isikeyiti}; ISIQINISEKISO= {ibhola, isigwedlo, isikeyiti}
- C= {okumnandi}, S= {ukuqothula}; CUS = {okumnandi, ukuqeda}
- C= {okumnandi}, S= {ukuqothula}; T= {ibhodlela}, CUSUT = {margarita, i-carnation, ibhodlela}
- G= {okuluhlaza okotshani, okuluhlaza okwesibhakabhaka, okumnyama}, H= {mnyama}; GUH= {okuluhlaza okotshani, okuluhlaza okwesibhakabhaka, okumnyama}
- TO={ 1, 3, 5, 7, 9 }; B={ 10, 11, 12 }; AUB={ 1, 3, 5, 7, 9, 10, 11, 12 }
- UD= {NgoLwesibili, uLwesine}, FUTHI= {NgoLwesithathu, uLwesihlanu}; KUFANELE = {NgoLwesibili, uLwesithathu, uLwesine, uLwesihlanu}
- B= {umiyane, inyosi, umzwilili}; C= {inkomo, inja, ihhashi}; I-BUC= {umiyane, inyosi, i-hummingbird, inkomo, inja, ihhashi}
- TO={2, 4, 6, 8}, B={1, 2, 3, 4}; AUB={1, 2, 3, 4, 6, 8}
- P= {itafula, isihlalo}, Q= {itafula, isihlalo}; PUQ= {itafula, isihlalo}
- TO= {isinkwa}, B = {ushizi}; AUB= {isinkwa, ushizi}
- TO={20, 30, 40}, B= {5, 15}; AUB ={5, 15, 20, 30, 40}
- UM= {Januwari, Februwari, Mashi, Ephreli}, N= {Novemba, Disemba}; UMUNTU= {Januwari, Februwari, Mashi, Ephreli, Novemba, Disemba}
- F={12, 22, 32, 42}, G= {a, e, i, o, u}; FUG= {12, 22, 32, 42, a, e, i, o, u}
- TO= {ehlobo}, B= {ubusika}; AUB= {ihlobo, ubusika}
- S= {imbadada, ishelelisi, i-flip flop}, R= {ihembe}; ENINGIZIMU= {imbadada, isiliphu, i-flip flop, ihembe}
- H= {NgoMsombuluko, ngoLwesibili}, R= {NgoMsombuluko, ngoLwesibili}, UD= {NgoMsombuluko, ngoLwesibili}; HURUD= {NgoMsombuluko, ngoLwesibili}
- P= {okubomvu, okuluhlaza okwesibhakabhaka}, Q= {oluhlaza, okuphuzi}, PUQ= {obomvu, oluhlaza okwesibhakabhaka, oluhlaza okotshani, ophuzi}
