KARTEZYEN \u00c7ARPIM \u2013 BA\u011eINTI <\/p>\n
A. SIRALI n L\u0130
\n n tane nesnenin belli bir \u00f6ncelik s\u0131ras\u0131na g\u00f6re d\u00fczenlenip, tek bir nesne gibi d\u00fc\u015f\u00fcn\u00fclmesiyle elde edilen ifadeye s\u0131ral\u0131 n li denir.
\n (a, b) s\u0131ral\u0131 ikilisinde;
\n a : Birinci bile\u015fen,
\n b : \u0130kinci bile\u015fendir.<\/p>\n
a \u00b9 b ise, (a, b) \u00b9 (b, a) d\u0131r.
\n (a, b) = (c, d) ise, (a = c ve b = d) dir.
\n *
\n B. KARTEZYEN \u00c7ARPIM
\n A ve B herhangi iki k\u00fcme olmak \u00fczere, birinci bile\u015feni A k\u00fcmesinden, ikinci bile\u015feni B k\u00fcmesinden al\u0131narak olu\u015fturulan b\u00fct\u00fcn s\u0131ral\u0131 ikililerin k\u00fcmesine, A ile B nin kartezyen \u00e7arp\u0131m\u0131 denir.
\n A kartezyen \u00e7arp\u0131m B k\u00fcmesi A x B ile g\u00f6sterilir.
\n A x B = {(x, y) : x \u00ce A ve y \u00ce B** dir.<\/p>\n
A \u00b9 B ise, A x B \u00b9 B x A d\u0131r.
\n *
\n C. KARTEZYEN \u00c7ARPIMININ \u00d6ZEL\u0130KLER\u0130
\n ** I)* s(A) = m ve s(B) = n ise
\n ****** s(A x B) = s(B x A) = m . n dir.
\n * II) A x (B x C) = (A x B) x C
\n *III) A x (B \u00c8 C) = (A x B) \u00c8 (A x C)
\n *IV) (B \u00c8 C) x A = (B x A) \u00c8 (C x A)
\n * V) A x (B \u00c7 C) = (A x B) \u00c7 (A x C)
\n *VI) A x \u00c6 = \u00c6 x A = \u00c6
\n VII) <\/p>\n
D. BA\u011eINTI
\n A ve B herhangi iki k\u00fcme olmak \u00fczere A x B nin her alt k\u00fcmesine A dan B ye ba\u011f\u0131nt\u0131 denir.
\n Ba\u011f\u0131nt\u0131 genellikle b bi\u00e7iminde g\u00f6sterilir.
\n b \u00cc A x B ise, b = {(x, y) : (x, y) \u00ce A x B** dir.
\n *
\n ** s(A) = m ve s(B) = n ise,
\n *** A dan B ye 2m.n tane ba\u011f\u0131nt\u0131 tan\u0131mlanabilir.
\n *
\n ** A x A n\u0131n herhangi bir alt k\u00fcmesine A dan A ya ba\u011f\u0131nt\u0131 ya da A da ba\u011f\u0131nt\u0131 denir.
\n *
\n ** s(A) = m ve s(B) = n olmak \u00fczere,
\n *** A dan B ye tan\u0131mlanabilen r elemanl\u0131 (r \u00a3 m . n) ba\u011f\u0131nt\u0131 say\u0131s\u0131
\n ***
\n *
\n ** b \u00cc A x B olmak \u00fczere,
\n *** b = {(x, y) : (x, y) \u00ce A x B** ba\u011f\u0131nt\u0131s\u0131n\u0131n tersi
\n *** b-1 \u00cc B x A d\u0131r.
\n *** Buna g\u00f6re, b ba\u011f\u0131nt\u0131s\u0131n\u0131n tersi
\n *** b-1 = {(y, x) : (x, y) \u00ce b** d\u0131r.
\n *
\n E. BA\u011eINTININ \u00d6ZEL\u0130KLER\u0130
\n b, A da tan\u0131ml\u0131 bir ba\u011f\u0131nt\u0131 olsun.
\n *
\n 1. Yans\u0131ma \u00d6zeli\u011fi
\n A k\u00fcmesinin b\u00fct\u00fcn x elemanlar\u0131 i\u00e7in (x, x) \u00ce b ise, b yans\u0131yand\u0131r.
\n “x \u00ce A i\u00e7in, (x, x) \u00ce b \u00aa b yans\u0131yand\u0131r.
\n *
\n 2. Simetri \u00d6zeli\u011fi
\n b ba\u011f\u0131nt\u0131s\u0131n\u0131n b\u00fct\u00fcn (x, y) elemanlar\u0131 i\u00e7in (y, x) \u00ce b ise, b simetriktir.
\n “(x, y) \u00ce b i\u00e7in (y, x) \u00ce b \u00aa b simetriktir.
\n *
\n ** b ba\u011f\u0131nt\u0131s\u0131 simetrik ise b = b-1 dir.
\n ** s(A) = n olmak \u00fczere, A k\u00fcmesinde tan\u0131mlanabilecek simetrik ba\u011f\u0131nt\u0131 say\u0131s\u0131 dir.
\n ** s(A) = n olmak \u00fczere, A k\u00fcmesinde tan\u0131mlanabilecek yans\u0131yan ba\u011f\u0131nt\u0131 say\u0131s\u0131 2(n.n – n) dir.
\n *
\n 3. Ters Simetri \u00d6zeli\u011fi
\n b ba\u011f\u0131nt\u0131s\u0131 A k\u00fcmesinde tan\u0131ml\u0131 olsun.
\n x \u00b9 y iken “(x, y) \u00ce b i\u00e7in (y, x) \u00cf b ise, b ters simetriktir.
\n *<\/p>\n
b ba\u011f\u0131nt\u0131s\u0131nda (x, x) eleman\u0131n bulunmas\u0131 ters simetri \u00f6zeli\u011fini bozmaz.
\n *
\n 4. Ge\u00e7i\u015fme \u00d6zeli\u011fi
\n b, A da tan\u0131ml\u0131 bir ba\u011f\u0131nt\u0131 olsun.<\/p>\n
olmal\u0131
\n b ba\u011f\u0131nt\u0131s\u0131n\u0131n ge\u00e7i\u015fme \u00f6zelli\u011fi vard\u0131r.
\n *
\n F. BA\u011eINTI \u00c7E\u015e\u0130TLER\u0130
\n 1. Denklik Ba\u011f\u0131nt\u0131s\u0131
\n b ba\u011f\u0131nt\u0131s\u0131 A k\u00fcmesinde tan\u0131ml\u0131 olsun.
\n b; Yans\u0131ma, Simetri, Ge\u00e7i\u015fme \u00f6zelli\u011fini sa\u011fl\u0131yorsa denklik ba\u011f\u0131nt\u0131s\u0131d\u0131r.
\n *
\n * *b denklik ba\u011f\u0131nt\u0131s\u0131 ve (x, y) \u00ce b ise, x denktir. y ye denir.
\n *** x \u00ba y bi\u00e7iminde g\u00f6sterilir.
\n *
\n ** b denklik ba\u011f\u0131nt\u0131s\u0131 olmak \u00fczere A da a eleman\u0131na denk olan b\u00fct\u00fcn elemanlar\u0131n k\u00fcmesine a n\u0131n denklik s\u0131n\u0131f\u0131 denir.
\n *** bi\u00e7iminde g\u00f6sterilir.
\n *** Buna g\u00f6re, a n\u0131n denklik s\u0131n\u0131f\u0131n\u0131n k\u00fcmesi,
\n *** = {y : y \u00ce A ve (a, y) \u00ce b** olur.
\n *
\n 2. S\u0131ralama Ba\u011f\u0131nt\u0131s\u0131
\n A k\u00fcmesinde tan\u0131ml\u0131 b ba\u011f\u0131nt\u0131s\u0131nda; Yans\u0131ma, Ters simetri, Ge\u00e7i\u015fme \u00f6zelli\u011fi varsa ba\u011f\u0131nt\u0131 s\u0131ralama ba\u011f\u0131nt\u0131s\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"
KARTEZYEN \u00c7ARPIM \u2013 BA\u011eINTI A. SIRALI n L\u0130 n tane nesnenin belli bir \u00f6ncelik s\u0131ras\u0131na g\u00f6re d\u00fczenlenip, tek bir nesne gibi d\u00fc\u015f\u00fcn\u00fclmesiyle elde edilen ifadeye s\u0131ral\u0131 n li denir. (a, b) s\u0131ral\u0131 ikilisinde; a : Birinci bile\u015fen, b : \u0130kinci bile\u015fendir. a \u00b9 b ise, (a, b) \u00b9 (b, a) d\u0131r. (a, b) = (c, …<\/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":[3543,7353,7350,7351,7352],"class_list":["post-3134","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-alt-kume","tag-gecisme-ozeligi","tag-kartezyen-carpim","tag-simetri-ozeligi","tag-ters-simetri-ozeligi"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3134","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=3134"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3134\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}