A. TANIM Herhangi bir A k\u00fcmesinden A k\u00fcmesine tan\u0131mlanan her fonksiyona birli i\u015flem denir.
\n A \u00cc B olmak \u00fczere, A x A k\u00fcmesinden B k\u00fcmesine tan\u0131mlanan her fonksiyona ikili i\u015flem veya k\u0131saca i\u015flem denir.
\n\u0130\u015femler; + , \u2013 , : , x, D ,o,\u00a8 , *, \u00ab gibi simgelerle g\u00f6sterilir.B. \u0130\u015eLEM\u0130N \u00d6ZELL\u0130KLER\u0130
\n A k\u00fcmesinde D ve * i\u015flemleri tan\u0131mlanm\u0131\u015f olsun. Buna g\u00f6re, a\u015fa\u011f\u0131daki 7 \u00f6zelli\u011fi inceleyelim.
\n1. Kapal\u0131l\u0131k \u00d6zelli\u011fi
\n” a, b \u00ce A i\u00e7in aDb nin sonucu A k\u00fcmesinin bir eleman\u0131 ise, A k\u00fcmesi Di\u015flemine g\u00f6re kapal\u0131d\u0131r.
\n2. De\u011fi\u015fme \u00d6zelli\u011fi
\n” a, b \u00ce A i\u00e7in, aD b = bD a ise, Di\u015fleminin de\u011fi\u015fme \u00f6zelli\u011fi vard\u0131r.
\n3. Birle\u015fme \u00d6zelli\u011fi
\n” a, b, c \u00ce A i\u00e7in aD (bD c) = (Da b) Dc ise,D i\u015fleminin birle\u015fme \u00f6zelli\u011fi vard\u0131r.
\n4. Birim (Etkisiz) Eleman \u00d6zelli\u011fi
\n” x \u00ce A i\u00e7in, xD e = e Dx = x ise, e ye Di\u015fleminin etkisiz eleman\u0131 denir.
\n e \u00ce A ise,D i\u015flemine g\u00f6re A k\u00fcmesi birim eleman \u00f6zelli\u011fine sahiptir.
\n5. Ters Eleman \u00d6zelli\u011fi
\nDi\u015fleminin etkisiz eleman\u0131 e olsun.
\n” a \u00ce A i\u00e7in, aD b = bD a = e olacak bi\u00e7imde bir b varsa b eleman\u0131na i\u015flemine g\u00f6re a n\u0131n tersi denir.
\n a n\u0131n tersi b ise genellikle b = a\u20131 bi\u00e7iminde g\u00f6sterilir.
\n b \u00ce A ise,D xi\u015flemine g\u00f6re A k\u00fcmesi ters eleman \u00f6zelli\u011fine sahiptir.
\nBirim eleman\u0131n tersi kendisine e\u015fittir.
\nTersi kendisine e\u015fit olan her eleman birim eleman olmayabilir.
\n6. Da\u011f\u0131lma \u00d6zelli\u011fi
\n” a, b, c \u00ce A i\u00e7in,
\n a * (bD c) = (a * b)D(a* c) ise,
\n* i\u015fleminin D i\u015flemi \u00fczerinde soldan da\u011f\u0131lma \u00f6zelli\u011fi vard\u0131r.
\n (aD b) * c = (a * c)D(b * c) ise,
\n* i\u015fleminin i\u015flemi \u00fczerinde sa\u011fdan da\u011f\u0131lma \u00f6zelli\u011fi vard\u0131r.
\n* i\u015fleminin D i\u015flemi \u00fczerinde; hem soldan, hem de sa\u011fdan da\u011f\u0131lma \u00f6zelli\u011fi varsa * i\u015fleminin D i\u015flemi \u00fczerinde da\u011f\u0131lma \u00f6zelli\u011fi vard\u0131r.
\n7. Yutan Eleman \u00d6zelli\u011fi
\n” x \u00ce A i\u00e7in, xDi y = yDx = y olacak bi\u00e7imde bir y varsa y ye Dii\u015fleminin yutan eleman\u0131 denir.
\n y \u00ce A ise,D i\u015flemine g\u00f6re A k\u00fcmesi yutan eleman \u00f6zelli\u011fine sahiptir.
\nYutan eleman\u0131n tersi yoktur. Fakat tersi olmayan her eleman yutan eleman de\u011fildir.
\nC. TABLO \u0130LE TANIMLANMI\u015e \u0130\u015eLEMLER<\/p>\n
A = {a, b, c, d} k\u00fcmesinde *\u00b6 i\u015flemi a\u015fa\u011f\u0131daki tablo ile tan\u0131mlanm\u0131\u015f olsun.<\/p>\n
\u00dc b * c nin sonucu bulunurken, ba\u015flang\u0131\u00e7 s\u00fctununda b, ba\u015flang\u0131\u00e7 sat\u0131r\u0131nda c bulunur. Bunlar\u0131n kesi\u015fti\u011fi b\u00f6lgedeki eleman, b *c nin sonucudur. Buna g\u00f6re, b * c = a d\u0131r.
\n\u00dc Ba\u015flang\u0131\u00e7 sat\u0131r\u0131ndaki ve ba\u015flang\u0131\u00e7 s\u00fctunundaki elemanlar\u0131n sonu\u00e7lar\u0131n\u0131n g\u00f6r\u00fcld\u00fc\u011f\u00fc k\u0131s\u0131mda A k\u00fcmesine ait olmayan eleman yoksa A k\u00fcmesi * i\u015flemine g\u00f6re kapal\u0131d\u0131r.
\n\u00dc Sonu\u00e7lar k\u0131sm\u0131, k\u00f6\u015fegene g\u00f6re simetrik ise, * i\u015fleminin de\u011fi\u015fme \u00f6zelli\u011fi vard\u0131r.
\n\u00dc Tablonun sonu\u00e7lar k\u0131sm\u0131nda ba\u015flang\u0131\u00e7 s\u00fctununun ve ba\u015flang\u0131\u00e7 sat\u0131r\u0131n\u0131n g\u00f6r\u00fcld\u00fc\u011f\u00fc s\u00fctunun ve sat\u0131r\u0131n kesi\u015fimin deki eleman etkisiz elemand\u0131r.
\n\u00dc Yutan eleman hangi elemanla i\u015fleme girerse girsin, sonu\u00e7 kendisine e\u015fit olur. Bunun i\u00e7in, tablonun sonu\u00e7lar k\u0131sm\u0131nda ayn\u0131 elemandan olu\u015fan sat\u0131r ve s\u00fctun belirlenir. Bulunan yutan elemand\u0131r.<\/p>\n
D. MATEMAT\u0130K S\u0130STEMLER
\n1. Tan\u0131m
\n A, bo\u015f olmayan bir k\u00fcme olmak \u00fczere, * i\u015flemi A da tan\u0131ml\u0131 olsun.
\n (A, *) ikilisine matematik sistem denir.
\n2. Grup
\n A \u00b9 \u00c6 olmak \u00fczere, A k\u00fcmesinde tan\u0131ml\u0131 * i\u015flemi a\u015fa\u011f\u0131daki d\u00f6rt ko\u015fulu sa\u011fl\u0131yorsa, A k\u00fcmesi* i\u015flemine g\u00f6re bir gruptur.
\nA, * i\u015flemine g\u00f6re kapal\u0131d\u0131r.
\nA \u00fczerinde * i\u015fleminin birle\u015fme \u00f6zelli\u011fi vard\u0131r.
\nA \u00fczerinde * i\u015fleminin birim (etkisiz) eleman\u0131 vard\u0131r.
\nA \u00fczerinde *i\u015flemine g\u00f6re her eleman\u0131n tersi vard\u0131r.
\nA \u00fczerinde tan\u0131ml\u0131 * i\u015fleminin de\u011fi\u015fme \u00f6zelli\u011fi de varsa (A,*) sistemi de\u011fi\u015fmeli gruptur.3. Halka
\nA \u00b9\u00c6 olmak \u00fczere, A k\u00fcmesi \u00fczerinde tan\u0131ml\u0131 D ve * i\u015flemleri a\u015fa\u011f\u0131daki \u00fc\u00e7 ko\u015fulu sa\u011fl\u0131yorsa (A, D, *) sistemi bir halkad\u0131r.
\n(A, D) sistemi de\u011fi\u015fmeli gruptur.
\nA k\u00fcmesi*i\u015flemine g\u00f6re kapal\u0131d\u0131r.
\n*i\u015fleminin D i\u015flemi \u00fczerinde da\u011f\u0131lma \u00f6zelli\u011fi vard\u0131r.
\n\u00dc * i\u015fleminin de\u011fi\u015fme \u00f6zelli\u011fi de varsa (A, D, *) sistemi de\u011fi\u015fmeli halkad\u0131r.
\n\u00dc *i\u015fleminin A k\u00fcmesinde birim (etkisiz) eleman\u0131 da varsa (A, D, *) sistemine birim halka denir.<\/p>\n","protected":false},"excerpt":{"rendered":"
A. TANIM Herhangi bir A k\u00fcmesinden A k\u00fcmesine tan\u0131mlanan her fonksiyona birli i\u015flem denir. A \u00cc B olmak \u00fczere, A x A k\u00fcmesinden B k\u00fcmesine tan\u0131mlanan her fonksiyona ikili i\u015flem veya k\u0131saca i\u015flem denir. \u0130\u015femler; + , \u2013 , : , x, D ,o,\u00a8 , *, \u00ab gibi simgelerle g\u00f6sterilir.B. \u0130\u015eLEM\u0130N \u00d6ZELL\u0130KLER\u0130 A k\u00fcmesinde D …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7331,7211],"class_list":["post-3122","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-islem","tag-kume"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3122"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3122\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}