Mathematics 1 Deneme Sınavı Sorusu #1366774

Given that A={0,1,2,3,a,b}, how many subsets of A contains both letters( "a" and "b")?


7

8

16

31

32


Yanıt Açıklaması:

Let's combine a and b to single element that we call *. Then our set will become A={0,1,2,3,*}. Since this set has 5 elements it has 32 subsets (25=32). Out of these 32 sets, there are 16 sets that doesn't contain *. (If we delete *, there remains a set containing 4 elements which has 24=16 subsets). A subset will either contain * or it will not contain *. Thus 32-16=16 sets contain *, namely a and b.

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