Kafa ka'idar yanzu tana cikin ilimin lissafi. Dukanmu mun san cewa ana kiranta saiti kowane tarin abubuwa a bayyane yake rarrabewa daga juna, waɗanda ke da halaye ɗaya (ko fiye) na kowa. Kafa ka'idar tana nazarin kaddarori da alaƙar saiti; Bolzano da Cantor sun inganta wannan filin, sannan sauran masana ilimin lissafi, kamar Zermelo da Fraenkel sun kammala shi a cikin ƙarni na 20.
Yana da mahimmanci cewa kowane saiti an bayyana shi daidai, wato, ana iya kafa shi da madaidaici ko an ba shi abu, na sa ne ko a'a.
- Kunna lissafi wannan gabaɗaya kai tsaye ne. Misali, idan aka yi la’akari da saitin har ma da lambobin da suka fi 1 da ƙasa da 15, a bayyane yake cewa wannan saitin zai ƙunshi lambobi 2, 4, 6, 8, 10, 12 da 14 kawai.
- A harshe gama gari, yin magana game da ƙungiya na iya zama mafi ƙima, saboda idan muna son ƙirƙirar ƙungiyar mawaƙa mafi kyau, alal misali, ra'ayoyi za su bambanta kuma ba za a sami cikakkiyar yarjejeniya kan wanda zai kasance cikin wannan rukunin da wanda ba zai . Wasu saiti na musamman sune faranti marasa fa'ida (babu abubuwa) ko saiti ɗaya (tare da kashi ɗaya kawai).
The abubuwan da ke cikin saiti ana kiransu membobi ko abubuwa, da kuma saiti ana wakilta su a cikin rubutattun rubutun da aka haɗa cikin braces: {}. A cikin takalmin gyaran kafa, ana raba abubuwa da waƙafi. Hakanan ana iya wakiltar su ta hanyar zane -zanen Venn, waɗanda ke haɗa tarin abubuwan da ke haɗa kowane saiti a cikin madaidaici da rufaffiyar layi, gabaɗaya a cikin siffar da'irar. Lokacin da akwai da yawa daga cikin waɗannan layukan rufewa, kowannen su an ba shi babban harafi (A, B, C, da sauransu) kuma saitin duniya na waɗannan yana wakiltar harafin U, wanda ke nufin saitin duniya.
Tare da saiti za ku iya yi ayyuka; manyan su shine ƙungiya, tsaka -tsaki, banbanci, dacewa da samfurin Cartesian. Haɗin ƙungiyar biyu A da B an bayyana shi azaman saitin A ∪ B kuma wannan yana ƙunshe da kowane ɓangaren da ke cikin aƙalla ɗaya daga cikinsu. Babban jumlar da ke wakiltar ta ita ce:
- ZUWA= {José, Jerónimo}, B= {María, Mabel, Marcela}; AUB= {José, Jerónimo, María, Mabel, Marcela}
- P= {pear, apple}, C= {lemo, lemu}; F= {cherry, currant};PUCUF = {pear, apple, lemun tsami, orange, cherry, currant}
- M={7, 9, 11}, N={4, 6, 8}; MUN={7, 9, 11, 4, 6, 8}
- R= {ball, skate, paddle}, G= {kwale -kwale, kwallo, kankara}; RUG= {ball, paddle, skate}
- C= {daisy}, S= {karnci}; CUS = {daisy, carnation}
- C= {daisy}, S= {karnci}; T= {kwalba}, CUSUT = {margarita, carnation, kwalba}
- G= {kore, shuɗi, baƙi}, H= {baki}; GUH= {kore, shuɗi, baƙi}
- ZUWA={ 1, 3, 5, 7, 9 }; B={ 10, 11, 12 }; AUB={ 1, 3, 5, 7, 9, 10, 11, 12 }
- D= {Talata, Alhamis}, DA= {Laraba, Juma'a}; DUBI = {Talata, Laraba, Alhamis, Juma'a}
- B= {sauro, kudan zuma, hummingbird}; C= {saniya, kare, doki}; BUC= {sauro, kudan zuma, hummingbird, saniya, kare, doki}
- ZUWA={2, 4, 6, 8}, B={1, 2, 3, 4}; AUB={1, 2, 3, 4, 6, 8}
- P= {tebur, kujera}, Tambaya= {tebur, kujera}; PUQ= {tebur, kujera}
- ZUWA= {gurasa}, B = {cuku}; AUB= {gurasa, cuku}
- ZUWA={20, 30, 40}, B= {5, 15}; AUB ={5, 15, 20, 30, 40}
- M= {Janairu, Fabrairu, Maris, Afrilu}, N= {Nuwamba, Disamba}; MUN= {Janairu, Fabrairu, Maris, Afrilu, Nuwamba, Disamba}
- F={12, 22, 32, 42}, G= {a, e, i, o, u}; FUG= {12, 22, 32, 42, a, e, i, o, u}
- ZUWA= {bazara}, B= {hunturu}; AUB= {bazara, hunturu}
- S= {sandal, slipper, flip flop}, R= {riga}; KUDU= {sandal, slipper, flip flop, shirt}
- H= {Litinin, Talata}, R= {Litinin, Talata}, D= {Litinin, Talata}; HURUD= {Litinin, Talata}
- P= {ja, shuɗi}, Tambaya= {kore, rawaya}, PUQ= {ja, shuɗi, kore, rawaya}
