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derslerimizde kümeler ayrıntılı bir şekilde incelenmiştir.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1028333/de97d0ed7561265e947fd1318a6b809f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/LDz7KQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=videoid:13232883521919094604","teaser":[{"list":{"type":"unordered","items":["Bu video, bir öğretmenin matematik dersinde kümeler konusunu anlattığı eğitim içeriğidir. Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Videoda alt küme sayıları ve özalt küme sayıları konusu ele alınmaktadır. Öğretmen önce üç elemanlı alt küme sayısı beş elemanlı alt küme sayısına eşit olan bir kümenin eleman sayısını bulma sorusunu çözmekte, ardından \"en az\", \"en çok\" gibi ifadelerin alt küme sayılarında nasıl kullanıldığını açıklamaktadır. Ayrıca 16 elemanlı bir kümenin alt küme sayısını hesaplama ve A, B, C, D, E, F ve G elemanlarından oluşan bir kümede kaç tane A kümesi oluşabileceğini sormaktadır.","Öğretmen, konuyu ezberlemek yerine mantığını anlamayı vurgulamakta ve dersin sonunda 10 dakikalık bir ara verileceğini belirtmektedir. Video, kümelerin alt küme sayılarını hesaplama formüllerini ve bunların uygulamalarını içermektedir."]},"endTime":775,"title":"Kümeler ve Alt Küme Sayıları Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Alt Küme Sayısı Problemi","list":{"type":"unordered","items":["Üç elemanlı alt küme sayısı beş elemanlı alt küme sayısına eşit olan bir kümenin eleman sayısı sekizdir.","Sekiz elemanlı bir kümenin alt küme sayısı 2⁸ = 256'dır.","En az iki elemanlı alt küme sayısı, 8'in 2'li, 3'lü, 4'lü ve 8'li kombinasyonlarının toplamı olan 247'dir."]},"beginTime":0,"endTime":173,"href":"/video/preview/13232883521919094604?parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=2Alt&t=0&ask_summarization=1"},{"index":1,"title":"Farklı Alt Küme Sayıları","list":{"type":"unordered","items":["En çok iki elemanlı alt küme sayısı, 8'in 0'lı, 1'li ve 2'li kombinasyonlarının toplamı olan 29'dur.","En az yedi elemanlı alt küme sayısı, 8'in 7'li ve 8'li kombinasyonlarının toplamı olan 9'dur.","En çok bir elemanlı alt küme sayısı, 8'in 0'lı ve 1'li kombinasyonlarının toplamı olan 9'dur."]},"beginTime":173,"endTime":305,"href":"/video/preview/13232883521919094604?parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=2Alt&t=173&ask_summarization=1"},{"index":2,"title":"Marmara Kelimesi Problemi","list":{"type":"unordered","items":["Marmara kelimesinin harflerinden oluşan küme üç elemanlıdır: M, A, R.","Bu üç elemanlı kümenin alt küme sayısı 2³ = 8, özalt küme sayısı 2³ - 1 = 7'dir.","Alt küme sayısı özalt küme sayısının 8/7 katıdır."]},"beginTime":305,"endTime":527,"href":"/video/preview/13232883521919094604?parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=2Alt&t=305&ask_summarization=1"},{"index":3,"title":"Küme Alt Küme İlişkisi","list":{"type":"unordered","items":["A ⊆ B koşulunu sağlayan A kümesi, B kümesinin tüm alt kümelerini içerir.","A kümesi boş küme olabilir, sadece B kümesinin elemanları olabilir veya B kümesinin tüm elemanları ile birlikte başka elemanlar da olabilir.","A kümesi, B kümesinin tüm alt küme sayısını verir."]},"beginTime":527,"endTime":669,"href":"/video/preview/13232883521919094604?parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=2Alt&t=527&ask_summarization=1"},{"index":4,"title":"Alt Küme Sayısı Hesaplama","list":{"type":"unordered","items":["Bir kümenin alt küme sayısı, o kümenin eleman sayısının 2'nin kuvveti olarak hesaplanır.","Örneğin, 16 elemanlı bir kümenin alt küme sayısı 2¹⁶'dır.","Sınavlarda bu hesaplamaları uzun süre yapmadan, mantığı anlayarak hızlıca yapabilirsiniz."]},"beginTime":685,"endTime":702,"href":"/video/preview/13232883521919094604?parent-reqid=1769690851192257-5675036453921827829-balancer-l7leveler-kubr-yp-klg-74-BAL&text=2Alt&t=685&ask_summarization=1"},{"index":5,"title":"Alt Küme Mantığı","list":{"type":"unordered","items":["Bir kümenin 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