Business Essay

1377 words - 6 pages

KÜMELERLE İLGİLİ SORU VE ÇÖZÜMLERSORU: A- ( B U C ) = (A-B ) ∩ ( A-C ) eşitliğinin doğruluğunu gösterelim.ÇÖZÜM: A-(B U C) = A∩ (B U C) '= A ∩( B ∩ C' ) (A-B = A ∩ B' olduğundan)= (A ∩ A) ∩ (B' ∩ C') ( De morgan kuralı )= (A ∩ B') ∩ (A ∩ C') ( Tek kuvvet özeliği )= (A-B) ∩ (A-C) bulunur. (kesişim işlemi birleşme özeliği)SORU: ( A-B )' kümesinin A' U B kümesine eşit olduğunu bulalım.ÇÖZÜM: ( A - B )' = ( A ∩ B' )'= A' U ( B' )' ( ( A - B ) = A ∩ B' idi )= A' U B Olur. ( De morgan kuralı )= ( A - B )' = A' U B Olur.SORU: A ve B iki kümedir. s( A ) = 2 . s( B ) , s( A - B ) = 10 ve A ∩ B kümesinin Alt kümelerinin sayısı 64 olduğuna göre,B kümesinin eleman sayısını bulalım .ÇÖZÜM : A ∩ B kümesinin alt kümelerinin sayısı 64 olduğuna göre,2n = 64 = 26 ( n = 6 bulunur. = 10 + 6 = 16 olur.s( A ∩ B ) = 6 olur. s( A ) = 2 . s ( B )s( A ) = s( A - B ) + s ( A ∩ B ) 16 = 2 . s( B ) ( s( B ) = 8 bulunur.SORU: s( A ) = 10 , s( B ) = 9 , s ( A U B ) = 15 ise s ( A - B )'yi bulalımÇÖZÜM : s( A ∩ B ) = x olsun A Bs( A U B ) = s( A ) + s( B ) -s( A ∩ B )15 = 10 + 9 - xx = 4 olur.s( A - B ) = s( A ) - s( A ∩ B )= 10 - 4 = 6 olur.SORU: Bir turist gurubu Almanca ve İngilizce dillerinden en az birini bilenlerden oluşmuştur. Grubun % 60'ı almanca, % 80'ni ingilizce biliyor.Grupta her iki dili konuşan 8 kişi vardır. Bu turist grubunda kaç kişi vardır?ÇÖZÜM: Grubu 100 kişi kabul edelims( A U İ ) = s( A ) + s( İ ) - s( A ∩ İ ) 40 8 kişi karşılık gelirse100 = 60 + 80 - s( A ∩ İ ) 100 X kişi karşılık gelir.( s( A ∩ İ ) = 40 x = 100 ٠ 8 = 2040SORU: İngizce veya Almanca dillerinden en az birinin bilindiği 34 kişilik bir turist grubunda sadece İngilizce bilenlerin sayısı, her iki dili bilenlerin 4 katından 1 fazladır. Bu grupta İngilizce bilen en fazla kaç kişi vardır?ÇÖZÜM: A X + Y + Z = 34X = 4Y + 1X + Y + Z = 4Y + 1 + Y + Z = 5Y + Z + 1 = 345Y=33-Z Z en küçük olduğunda ingilizcebilenler en fazla olur.O halde Z=3 olmalıdır.Z = 3 ( 5Y = 33 - 2 = 33 - 3 = 30 ( Y = 0En fazla İngilizce bilenlerin sayısı : X + Y = 4Y + 1 + Y = 5Y + 1 = 5٠6 + 1 = 31'dir.SORU : 40 kişik bir grupta, 8 kişi futbol ve basketbol oynamaktadır.30 kişi bu oyunlardan en az birini oynamaktadır. Futbol oynayanların sayısı basketbol oynayanların sayısından 6 fazladır. Bu grupta futbol...

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