Aragtida dejintu hadda waxay ka mid tahay xisaabta. Waxaan wada ognahay in loogu yeero go'an ururinta walxo kasta oo si cad loo kala sooci karo, kuwaas oo leh hal (ama ka badan) astaamo ay wadaagaan. Aragtida dejintu waxay dersaa sifooyinka iyo cilaaqaadyada qaybaha; Goobtan waxaa dallacsiiyay Bolzano iyo Cantor, ka dibna qummanaa qarnigii 20aad oo ay sameeyeen xisaabiyeyaasha kale, sida Zermelo iyo Fraenkel.
Waxaa muhiim ah in set kasta si fiican loo qeexo, taas oo ah, in lagu dhisi karo si sax ah ha ahaato shay, wuxuu ka tirsan yahay iyo in kale.
- Daaran xisaabta tani guud ahaan waa toos. Tusaale ahaan, haddii tirada tirooyinka ka weyn 1 iyo in ka yar 15 la tixgeliyo, way caddahay in setkan uu ka koobnaan doono lambarrada 2, 4, 6, 8, 10, 12 iyo 14 oo keliya.
- At luqad guud, ka hadlida koox waxay noqon kartaa wax aan sax ahayn, maxaa yeelay haddii aan rabno inaan samayno kooxda heesayaasha ugu fiican, tusaale ahaan, fikradaha way kala duwanaan doonaan mana jiri doonto isku raac buuxa oo ku saabsan cidda ka mid noqon doonta kooxdan iyo cidda aan ka mid noqon doonin . Qaar ka mid ah qaybaha gaarka ah ayaa ah qaybo madhan (oo aan lahayn waxyaalo) ama qaybo isku mid ah (oo leh hal cunsur).
The walxaha ka mid ah gogosha waxaa lagu magacaabaa xubno ama xubno, iyo xirmooyinka waxaa lagu matalayaa qoraalo qoran oo ku lifaaqan xargaha: {}. Gudaha kabka, alaabta waxaa lagu kala saaraa kooma. Waxa kale oo lagu meteli karaa jaantusyada Venn, kuwaas oo ku lifaaqan uruurinta walxaha ka samaysan mid kasta oo ku jira xariiq adag oo xidhan, guud ahaan qaabka goobada. Markay jiraan dhowr ka mid ah khadadkaan xiran, mid walba waxaa loo qoondeeyay xaraf weyn (A, B, C, iwm.) Iyo set -ka caalamiga ah ee kuwan waxaa matalaya xarafka U, oo macnaheedu yahay set guud.
Iyada oo la adeegsanayo waxaad samayn kartaa hawlgallada; kuwa ugu waaweyn waa ururka, isgoyska, farqiga, dhammaystirka iyo wax soo saarka Cartesian. Midowga laba qaybood A iyo B ayaa lagu qeexay inay yihiin set A ∪ B tanna waxaa ku jira walxo kasta oo ugu yaraan mid ka mid ah. Isleegga guud ee matala waa:
- KU= {José, Jerónimo}, B= {María, Mabel, Marcela}; AUB= {José, Jerónimo, María, Mabel, Marcela}
- P= {pear, tufaax}, C= {liin, oranji}; F= {cherry, currant};PUCUF = {pear, tufaax, liin, oranji, cherry, currant}
- M={7, 9, 11}, N={4, 6, 8}; MUN={7, 9, 11, 4, 6, 8}
- R= {kubbadda barafka, barafka lagu ciyaaro, boodboodka}, G= {taangiga, kubbada, barafka}; RUG= {kubbadda, barafka, barafka}
- C= {daisy}, S= {carnation}; CUS = {daisy, carnation}
- C= {daisy}, S= {carnation}; T= {dhalada}, CUSUT = {margarita, carnation, dhalo}
- G= {cagaar, buluug, madow}, H= {madow}; GUH= {cagaar, buluug, madow}
- KU={ 1, 3, 5, 7, 9 }; B={ 10, 11, 12 }; AUB={ 1, 3, 5, 7, 9, 10, 11, 12 }
- D= {Talaado, Khamiis}, IYO= {Arbaco, Jimce}; DHAMAAN = {Talaado, Arbaco, Khamiis, Jimce}
- B= {kaneeco, shinni, hummingbird}; C= {sac, ey, faras}; BUC= {kaneeco, shinni, hummingbird, lo, ey, faras}
- KU={2, 4, 6, 8}, B={1, 2, 3, 4}; AUB={1, 2, 3, 4, 6, 8}
- P= {miiska, kursi}, S= {miiska, kursi}; PUQ= {miiska, kursi}
- KU= {rooti}, B = {farmaajo}; AUB= {rooti, farmaajo}
- KU={20, 30, 40}, B= {5, 15}; AUB ={5, 15, 20, 30, 40}
- M= {Janaayo, Febraayo, Maarso, Abriil}, N= {Nofeembar, December}; MUN= {Janaayo, Febraayo, Maarso, Abriil, Noofambar, Diisambar}
- F={12, 22, 32, 42}, G= {a, e, i, o, u}; FUG= {12, 22, 32, 42, a, e, i, o, u}
- KU= {xagaaga}, B= {jiilaal}; AUB= {xagaaga, jiilaalka}
- S= {kabo, siibasho, flip flop}, R= {shaati}; KOONFUR= {kabo, siibasho, flip flip, shaati}
- H= {Isniin, Talaado}, R= {Isniin, Talaado}, D= {Isniin, Talaado}; HURUD= {Isniin, Talaado}
- P= {casaan, buluug}, S= {cagaar, jaalle}, PUQ= {casaan, buluug, cagaar, huruud}
