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İçerikte doğal sayılar, pozitif ve negatif üslü ifadeler, pozitif sayıların tüm kuvvetlerinin pozitif olması, negatif sayıların çift kuvvetlerinde eksi işaretinin kalktığı ve tek kuvvetlerinde eksi işaretinin kaldığı gibi temel prensipler örneklerle açıklanmaktadır.","Videoda ayrıca özel işlemler tanımlaması, üslü ifadelerin değerlerini hesaplama ve her zaman doğru olan ifadeleri belirleme gibi farklı soru tipleri çözülmektedir. Video, üslü sayılar konusunun birinci adımının tamamlanmasıyla sona ererken, ikinci videoda tüm ayrıntıların, tanımların, kavramların ve ispatların anlatılacağı bilgisi verilmektedir."]},"endTime":1719,"title":"9. Sınıf Matematik Dersi: Üslü Sayılar","beginTime":0}],"fullResult":[{"index":0,"title":"9. 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başlanacak."]},"beginTime":117,"endTime":251,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=117&ask_summarization=1"},{"index":2,"title":"Üslü Sayıların Tanımı","list":{"type":"unordered","items":["Üslü sayı, a'dan farklı bir gerçel sayı ve n'den pozitif bir tam sayı olmak üzere a üssü n ifadesine üslü gösterim adı verilir.","a üssü n ifadesinde a taban, n ise üs olarak adlandırılır ve a sayısının n tane yan yana çarpımı anlamına gelir.","5+5+5+5+5 ifadesi 5 üzeri 5 ile karıştırılmamalı, bu ifade 5×5×5×5×5 anlamına gelir."]},"beginTime":251,"endTime":333,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=251&ask_summarization=1"},{"index":3,"title":"Üslü Sayıların Özel Durumları","list":{"type":"unordered","items":["a'dan farklı olmak üzere a üssü 0, sıfır hariç bir sayının üstüne yazıldığında o 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5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×5×"]},"beginTime":416,"endTime":531,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=416&ask_summarization=1"},{"index":5,"title":"Doğal Sayılar ve Üslü İfadeler","list":{"type":"unordered","items":["Doğal sayılar sıfırdan başlayıp bir, iki, üç şeklinde artı sonsuza kadar giden sayılardır.","a ve b doğal sayı olmak üzere, a üzeri b = 81 olduğunda, bu koşulu sağlayan a+b toplamının alabileceği en küçük değer 7, en büyük değer 11'dir.","81'in farklı üslü ifadeleri 9² ve 3⁴'tür, bu değerlerin toplamı 89'dur."]},"beginTime":533,"endTime":632,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=533&ask_summarization=1"},{"index":6,"title":"Negatif Üsler","list":{"type":"unordered","items":["Bir ifadenin üstüne negatif bir üs yazıldığında, amaç sayıya takla attırmaktır.","a üzeri eksi n, 1 bölü a üzeri n anlamına gelir.","Örneğin, 3 üzeri eksi 2, 1 bölü 3 üzeri 2 demektir ve sonucu 1/9'dur."]},"beginTime":632,"endTime":679,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=632&ask_summarization=1"},{"index":7,"title":"Üslü Sayılar Kuralları","list":{"type":"unordered","items":["Pozitif sayıların tüm kuvvetleri pozitiftir, örneğin 3'ün herhangi bir kuvveti pozitiftir.","Negatif sayıların çift kuvveti alındığında içerideki eksi işareti kaybolur ve sonuç pozitif olur.","Negatif sayıların tek kuvveti alındığında içerideki eksi işareti korunur ve sonuç negatif olur."]},"beginTime":681,"endTime":766,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=681&ask_summarization=1"},{"index":8,"title":"Üslü Sayılar Örnekleri","list":{"type":"unordered","items":["(-3)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç -81 olur.","(-5)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç -625 olur.","(-2)⁴ ifadesinde üst çift sayı olduğu için eksi işareti kaybolur ve sonuç 16 olur."]},"beginTime":766,"endTime":872,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=766&ask_summarization=1"},{"index":9,"title":"Negatif Üslü Sayılar","list":{"type":"unordered","items":["4⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 2² = 16 olur.","(-5)⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 5² = 25 olur.","(-1/3)⁻⁴ ifadesinde üst negatif olduğu için sayı ters çevrilir ve 3⁴ = 81 olur."]},"beginTime":872,"endTime":980,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=872&ask_summarization=1"},{"index":10,"title":"Tanımsız İfadeler","list":{"type":"unordered","items":["0, 0'a bölünemez çünkü 0'ı elde etmek için çarpılacak sayı yoktur.","0, 0'a bölünemez ve bu durum matematikte tanımsızdır.","Tanımsız, bir şeyin tanımlanmamış olduğu anlamına gelir."]},"beginTime":980,"endTime":1014,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=980&ask_summarization=1"},{"index":11,"title":"Karmaşık Üslü Sayılar","list":{"type":"unordered","items":["2⁻² ifadesinde üst negatif olduğu için sayı ters çevrilir ve 1/2 olur.","(-3)⁻¹ ifadesinde üst negatif olduğu için sayı ters çevrilir ve -1/3 olur.","(-5)⁻¹ ifadesinde üst negatif olduğu için sayı ters çevrilir ve -1/5 olur."]},"beginTime":1014,"endTime":1141,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1014&ask_summarization=1"},{"index":12,"title":"Değişkenli Üslü Sayılar","list":{"type":"unordered","items":["a = 2 ve b = -3 olduğunda a⁻³ + b⁻² ifadesi hesaplanır.","Bir sayının üstüne üs yazıldığında parantezli yazmak zorunludur.","a⁻³ = 1/8 ve b⁻² = 1/9 olduğundan toplamları 1/8 + 1/9 = 1/72 olur."]},"beginTime":1141,"endTime":1236,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1141&ask_summarization=1"},{"index":13,"title":"Soru Avcısı Bölümü","list":{"type":"unordered","items":["Üslü sayıların birinci adım testi (soru avcısı testi) ile konu pekiştirilir.","(-2)² = 4, (-3)² = 9, (-1)² = 1 ve (-2)³ = -8 gibi temel üslü sayı değerleri kullanılır.","Üslü sayılarla ilgili basit işlemler hızlıca çözülür."]},"beginTime":1236,"endTime":1309,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1236&ask_summarization=1"},{"index":14,"title":"Üslü Sayılar Soruları","list":{"type":"unordered","items":["İlk soruda a-2b=2 eşitliği verilmiş ve (a-2)²+b² ifadesinin değeri sorulmuş, cevap 31/4 olarak bulunmuş.","İkinci soruda k⊕r=m şeklinde bir işlem tanımlanmış ve 9⊕5+3⊕2 işleminin sonucu 9 olarak hesaplanmış.","Üçüncü soruda abc tam sayı olmak üzere verilen bir simge tanımlanmış ve işlemin sonucu -17/12 olarak bulunmuş."]},"beginTime":1311,"endTime":1565,"href":"/video/preview/3183188314363314493?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1311&ask_summarization=1"},{"index":15,"title":"Özel Üslü Sayı Sorusu","list":{"type":"unordered","items":["Son soruda a bir tamsayı olmak üzere a¹=a, a⁻¹=1/a ve a⁻²=1/a² ifadelerinden hangilerinin her zaman doğrudur sorulmuş.","a⁻¹=1/a ifadesi her zaman doğrudur çünkü a⁻¹=1/a² ifadesi tanımsızdır.","Video, üslü sayılar konusunun birinci adımının sonuna gelmiş ve ikinci videoda tüm ayrıntılarıyla devam edileceği 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Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Videoda kümelerin temel kavramları detaylı şekilde ele alınmaktadır. İlk olarak kümenin tanımı ve gösterim yöntemleri (liste yöntemi, Venn şeması yöntemi ve ortak özellik yöntemi) anlatılmakta, ardından küme çeşitleri (sonlu ve sonsuz kümeler), boş küme, mutlak değer ve evrensel küme kavramları açıklanmaktadır. Son bölümde ise alt küme kavramı, alt küme sayısının hesaplanması ve iki kümenin eşitliği konuları işlenmektedir.","Öğretmen, konuları örneklerle pekiştirmekte ve sınavlarda çıkabilecek soru tiplerini göstermektedir. Video sonunda öğretmen, bir sonraki derste kesişim ve birleşim konusunu işleyeceğini belirtmektedir."]},"endTime":2705,"title":"Kümelerde Temel Kavramlar Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kümeler Konusuna Giriş","list":{"type":"unordered","items":["Kümelerde temel kavramlar konusuna başlanacak.","Bugün kümenin tanımı, küme gösterimleri, küme çeşitleri, alt küme ve eşit kümeler konuları ele alınacak.","Ders öncesi mantık konusunun bitirildiği ve bileşik önermeler, ve, veya, ya da, ise, ancak ve ancak kavramlarının öğrenildiği belirtiliyor."]},"beginTime":1,"endTime":81,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1&ask_summarization=1"},{"index":1,"title":"Küme Tanımı","list":{"type":"unordered","items":["Küme, iyi tanımlanmış nesneler topluluğudur.","İyi tanımlanmış nesneler, herkes için aynı şekilde anlaşılır ve belirli olan nesnelerdir (örneğin yaz ayları: Haziran, Temmuz, Ağustos).","Küme belirtmeyen örnekler: \"ondan küçük doğal sayılar\" (sınır belirtilmediği için), \"bazı günler\" (kişiye göre değişebilir), \"güzel kitaplar\" (tadıma dayalı)."]},"beginTime":81,"endTime":168,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=81&ask_summarization=1"},{"index":2,"title":"Küme Elemanları ve Gösterimi","list":{"type":"unordered","items":["Kümenin her bir nesnesine \"eleman\" denir.","Kümeler genellikle büyük harflerle gösterilir (A, B, C).","Bir kümenin eleman sayısı |A| şeklinde gösterilir.","Bir elemanın küme elemanı olması durumu a ∈ A şeklinde, eleman olmaması durumu a ∉ A şeklinde gösterilir."]},"beginTime":168,"endTime":318,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=168&ask_summarization=1"},{"index":3,"title":"Küme 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kullanılır."]},"beginTime":388,"endTime":701,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=388&ask_summarization=1"},{"index":5,"title":"Küme Çeşitleri","list":{"type":"unordered","items":["Küme çeşitleri arasında sonlu ve sonsuz kümeler bulunur.","Eleman sayısı sınırlı ve sayılabilen kümeler sonlu kümedir.","Eleman sayısı sınırlı olmayan ve sayılabilen sonu olmayan kümeler sonsuz kümedir."]},"beginTime":701,"endTime":938,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=701&ask_summarization=1"},{"index":6,"title":"Kümeler ve Örnekler","list":{"type":"unordered","items":["Bir tam sayının karesi 16'dan küçük olduğunda, bu tam sayılar 0, 1, 2, 3, -1, -2 ve -3 olabilir.","Bu küme 7 elemanlı bir sonlu kümedir.","Boş küme, elemanı olmayan kümeye denir ve ∅ veya {} şeklinde 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küme, bir V şeması içinde gösterildiğinde, içindeki tüm kümeleri kapsayan en büyük kümedir.","Alt küme, bir kümenin her elemanının aynı zamanda başka bir kümenin elemanı olduğu durumdur."]},"beginTime":1180,"endTime":1636,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1180&ask_summarization=1"},{"index":9,"title":"Alt Küme Özellikleri","list":{"type":"unordered","items":["Boş küme her kümenin alt kümesidir.","Her küme kendisinin alt kümesidir.","En elemanlı bir kümenin alt küme sayısı 2ⁿ'dir, özalt küme sayısı ise 2ⁿ⁻¹'dir."]},"beginTime":1636,"endTime":1777,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1636&ask_summarization=1"},{"index":10,"title":"Alt Küme Örnekleri","list":{"type":"unordered","items":["Alt küme, bir kümenin elemanlarından istediğimiz kadarını seçerek 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elemanlı alt kümeler yazılabilir (örneğin AB, BC).","Üç elemanlı alt küme, kümenin kendisidir."]},"beginTime":1871,"endTime":1936,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1871&ask_summarization=1"},{"index":13,"title":"Alt Küme Sayısı","list":{"type":"unordered","items":["Verilen örnekte toplam 8 alt küme bulunmaktadır.","Alt küme sayısı sadece sayılabilir, ayrı ayrı yazılmalıdır."]},"beginTime":1936,"endTime":1977,"href":"/video/preview/8052227461875322527?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1936&ask_summarization=1"},{"index":14,"title":"Soru Çözümü","list":{"type":"unordered","items":["Alt küme küme şeklinde gösterilir ve süslü parantez içermelidir.","Elemanlar süslü parantez içinde yazılır ve virgülle ayrılabilir.","Soruda 3 tanesi doğru cevap olarak 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Matematik yeni müfredata uygun Mantık Full Tekrar sınava hazırlık sınav öncesi son tekrar konu anlatım ve soru çözümleri yaptığımız dersimizde tüm konuyu tekrar edip sorular çözdük.","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2976818/c065341af8c00071f27dca336590d6c0/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/CQ8VPwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"15","reqid":"1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=videoid:4709542953985549559","teaser":[{"list":{"type":"unordered","items":["Bu video, Mehmet Hoca tarafından Rehber Matematik kanalında sunulan, mantık konusunu kapsamlı şekilde ele alan bir eğitim içeriğidir.","Video, mantık konusunun temel kavramlarından başlayarak ileri seviye konulara kadar uzanan bir yapıya sahiptir. Önermenin tanımı, doğruluk değerleri, bileşik önermeler (ve, veya, ya da, ise, ancak ve ancak), niceleyiciler, De Morgan kuralları, karşıt ve ters önermeler gibi konular detaylı olarak anlatılmaktadır. Ayrıca mantık tablolarının nasıl doldurulacağı ve sınavlarda çıkabilecek soru tipleri örneklerle açıklanmaktadır.","Video, on videoluk bir serinin son bölümü olup, bir sonraki derste kümeler konusunun işleneceği belirtilmektedir. Sınav öncesi tekrar yapmak isteyen öğrenciler için hazırlanmış olup, mantık konusunda temel bilgileri pekiştirmek isteyenler için faydalı bir kaynak niteliğindedir."]},"endTime":2323,"title":"Mantık Full Tekrar Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Mantık Full Tekrar Giriş","list":{"type":"unordered","items":["Mehmet hocanın sunduğu bu video, mantık konusunu baştan sona tarayan bir full tekrar videosudur.","Normalde Rehber Matematik kanalında 10 videoluk bir seri ile mantık konusu tanımlarla, kavramlarla ve ispatlarla detaylı olarak işlenmiş olup, bu video sınav öncesi son tekrar niteliğindedir.","Mantık konusunu baştan sona tarayarak sınav öncesi son tekrar yapmak için bu video izlenmelidir."]},"beginTime":0,"endTime":52,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=0&ask_summarization=1"},{"index":1,"title":"Önerme ve Doğruluk Değeri","list":{"type":"unordered","items":["Doğru ya da yanlış kesin hüküm bildiren ifadelere önerme adı verilir (örneğin: \"Bugün hava bulutlu\", \"Liverpool geçen sene şampiyon oldu\", \"Filler uçabilen hayvanlardır\").","Bir önerme ya doğrudur (1 ile gösterilir) ya da yanlıştır (0 ile gösterilir).","n tane önermenin 2 üzeri n tane doğruluk değeri vardır."]},"beginTime":52,"endTime":152,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=52&ask_summarization=1"},{"index":2,"title":"Denk Önermeler ve Olumsuzluk","list":{"type":"unordered","items":["İki önerme birbirine denkse, doğruluk değerleri aynıdır ve p ≡ q şeklinde gösterilir.","Bir önermenin olumsuzu (değili), önermenin hükmünün değiştirilmesiyle elde edilen önermedir.","Bir önermenin olumsuzluğunun olumsuzu, kendisine denktir (¬(¬p) ≡ p)."]},"beginTime":152,"endTime":250,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=152&ask_summarization=1"},{"index":3,"title":"Bileşik Önermeler ve Bağlaçlar","list":{"type":"unordered","items":["Bileşik önermeler, ve, veya, ya da, ise, ancak ve ancak bağlaçlarından meydana gelir.","\"Ve\" bağlacında, her iki önerme de doğru olduğunda sonuç doğru, diğer durumlarda sonuç yanlıştır.","\"Veya\" bağlacında, en az bir önerme doğru olduğunda sonuç doğru, ikisi de yanlış olduğunda sonuç yanlıştır.","\"Ya da\" bağlacında, iki önermenin değerleri birbirinden farklı olduğunda sonuç doğru, aynı olduğunda sonuç yanlıştır.","\"İse\" bağlacı 1011 değerlerine sahiptir ve \"Ancak ve ancak\" bağlacı \"Ya da\" bağlacının tam tersidir."]},"beginTime":250,"endTime":445,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=250&ask_summarization=1"},{"index":4,"title":"De Morgan Kuralları","list":{"type":"unordered","items":["De Morgan kuralları, bileşik önermelerin olumsuzluğunu almak için kullanılır.","\"Ve\" bağlacının olumsuzu, önermelerin olumsuzlarının \"Veya\" bağlacıyla birleşimidir.","\"Veya\" bağlacının olumsuzu, önermelerin olumsuzlarının \"Ve\" bağlacıyla birleşimidir."]},"beginTime":445,"endTime":476,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=445&ask_summarization=1"},{"index":5,"title":"Mantık Kuralları ve Bağlaçlar","list":{"type":"unordered","items":["De Morgan kuralları mantıkta önemli noktalardır ve sınavda gelme ihtimali yüksek olan konulardandır.","\"P ise q\" önermesinin denkliği \"p değil veya q\" şeklindedir.","\"P ise q\" önermesinin karşıtı, tersi ve olumsuzu farklıdır; karşıtı ve tersi karıştırılmamalıdır."]},"beginTime":482,"endTime":561,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=482&ask_summarization=1"},{"index":6,"title":"Bağlaçların Özellikleri","list":{"type":"unordered","items":["Tersi, bağlacın üstlerine değil işaretini yazarak bulunur.","Karşıtı, hem yerlerin değiştirilmesi hem de üstlerine değil işaretinin yapıştırılmasıyla elde edilir.","\"P ancak ve ancak q\" önermesi \"p ise q ve q ise p\" şeklinde açılır."]},"beginTime":561,"endTime":717,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=561&ask_summarization=1"},{"index":7,"title":"Açık Önermeler ve Niceleyiciler","list":{"type":"unordered","items":["Açık önerme, en az bir tane değişken içeren ve değişkenin değerine göre doğruluğu değişen önermedir.","Evrensel niceleyici \"her\" anlamına gelir ve tamamın değerini alır.","Varlıksal niceleyici \"en az bir\" anlamına gelir ve en az bir değer anlamını taşır."]},"beginTime":717,"endTime":834,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=717&ask_summarization=1"},{"index":8,"title":"Niceleyicilerin Olumsuzluk Durumları","list":{"type":"unordered","items":["\"Her x için px\" önermesinin olumsuzu \"en az bir x için px'nin değili\" şeklindedir.","\"En az bir x için px\" önermesinin olumsuzu \"her x için px'nin değili\" şeklindedir.","Niceleyicilerin olumsuzluk durumları sınavda sıkça sorulan konulardandır."]},"beginTime":834,"endTime":903,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=834&ask_summarization=1"},{"index":9,"title":"Mantık Tabloları","list":{"type":"unordered","items":["Mantık konusunda tablo doldurma önemli bir konudur.","Tablo doldururken, bağlaçların değerlerini doğru şekilde kullanmak gerekir.","\"İse\" bağlacı sadece \"1 ise 0\" durumunda 0 değerini alır, diğer durumlarda 1 değerini alır."]},"beginTime":903,"endTime":985,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=903&ask_summarization=1"},{"index":10,"title":"Bağlaç Kullanımı ve Doğruluk Değerleri","list":{"type":"unordered","items":["\"Ya da\" bağlacı, iki seçenek arasında seçim gerektirdiğinde kullanılır; örneğin \"Ali ya da Ayşe gelsin\" ifadesinde ikisi birden gelmesi veya hiçbiri gelmemesi istenmiyor.","\"Ve\" bağlacı, iki önermenin her ikisinin de doğru olması durumunda kullanılır.","Doğruluk değerleri hesaplanırken, bağlacın türüne göre farklı kurallar uygulanır; örneğin \"ve\" bağlacında her iki önermenin de doğru olması gerekirken, \"ya da\" bağlacında birinin doğru olması yeterlidir."]},"beginTime":987,"endTime":1074,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=987&ask_summarization=1"},{"index":11,"title":"Mantık Sorularında Yaklaşım","list":{"type":"unordered","items":["Mantık sorularında iki tip soru tipi vardır: birincisi bir önermenin doğruluk değerlerini bulmak, ikincisi verilen doğruluk değerlerinden yeni önermelerin doğruluk değerlerini hesaplamak.","Soruları çözerken önce bağlacı tespit etmek gerekir; bağlacın türüne göre çözüm stratejisi belirlenir.","\"Ancak ve ancak\" bağlacında, her iki önermenin de aynı doğruluk değerine sahip olması gerekir."]},"beginTime":1074,"endTime":1305,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1074&ask_summarization=1"},{"index":12,"title":"Mantık Özellikleri ve Uygulamaları","list":{"type":"unordered","items":["Mantıkta birleşme ve dağılma özellikleri vardır; örneğin \"veya\" bağlacı, \"ve\" bağlacına çevrilebilir.","\"Veya\" bağlacında birleşme özelliği, \"veya\" bağlacının her iki tarafını da \"ve\" bağlacıyla bağlar.","Mantık sorularında, önce önermelerin doğruluk değerleri bulunur, sonra bu değerler yerine konularak yeni önermelerin doğruluk değerleri hesaplanır."]},"beginTime":1305,"endTime":1509,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1305&ask_summarization=1"},{"index":13,"title":"Mantık Konularının Tekrarı","list":{"type":"unordered","items":["Mantık konularının tekrarı yapılıyor ve önceki soru tipleri aynı yolda devam ediyor.","\"Ve\" bağlacında farklı değerler varsa cevap \"bir\" gelir, aksi halde cevap \"sıfır\" çıkıyor.","Mantık konularını tekrarlayıp soruları çözerken tüm bilgiler yerlerine oturuyor."]},"beginTime":1517,"endTime":1562,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1517&ask_summarization=1"},{"index":14,"title":"Denklik ve De Morgan Kuralı","list":{"type":"unordered","items":["P ve Q'nun değili ile R'nin denkliği inceleniyor ve \"veya\" bağlacı kullanılarak çözüm bulunuyor.","De Morgan kuralı uygulanarak önermelerin denkleri bulunuyor ve eşleştirme yapılıyor.","De Morgan kuralına göre \"ve\" bağlacı \"veya\" bağlacına dönüştürülebiliyor."]},"beginTime":1562,"endTime":1814,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1562&ask_summarization=1"},{"index":15,"title":"Bileşik Önermelerin En Sade Hali","list":{"type":"unordered","items":["Bileşik önermelerin en sade halini bulma sorularında içteki terimlere dikkat edilmesi gerekiyor.","\"Ancak ve ancak\" bağlacında her iki taraf da \"bir\" ise sonuç \"bir\" oluyor.","\"Ve\" bağlacında bir tane bile \"sıfır\" varsa, sonuç \"sıfır\" oluyor."]},"beginTime":1814,"endTime":1935,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1814&ask_summarization=1"},{"index":16,"title":"Açık Önermeler","list":{"type":"unordered","items":["Açık önermelerde doğruluk değerleri bulunuyor; x gördüğün yere belirli değerler yazarak ifadelerin doğruluğu kontrol ediliyor.","Örneğin, p(3), p(-1) ve p(6) ifadelerinin doğruluk değerleri hesaplanıyor.","Açık önermelerde nicelilerden soru gelirse, x'e değerler yazarak doğruluk değerleri bulunuyor."]},"beginTime":1935,"endTime":2035,"href":"/video/preview/4709542953985549559?parent-reqid=1769259740111345-4642874319448772842-balancer-l7leveler-kubr-yp-vla-176-BAL&text=9cesec&t=1935&ask_summarization=1"},{"index":17,"title":"Mantık Sorularında Karşıt ve Ters 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