Math 141 Ch 6 Part 2

Math 141 Ch 6 Part 2 - The Number of Elements in a Finite...

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The Number of Elements in a Finite Set Determined by counting all of the elements in the set. Denoted by n ( A ). Example : Given A ={0, 1, 5, 7}, B ={0,1,2,…,15}, and C ={ }, find a) n(A) b) n(B) c) n(C)
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Counting with Disjoint Sets If sets A and B are disjoint, then Example : If A = { a, b, c, d } and B = { e, f, g }, find . ( ) ( ) ( ) n A B n A n B ! = + ( ) n A B !
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Counting the Elements in the Union of Sets In general, for any two sets, A and B , ( ) ( ) ( ) ( ) n A B n A n B n A B ! = + " #
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In general, for any three sets, A, B, and C , ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) n A B C n A n B n C n A B n A C n B C n A B C ! ! = + + " # " # " # + # #
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Example : A store sold 100 hair dryers, of which fifty had variable heat, 65 had variable speed, and 96 had variable heat or speed. a) How many had both variable heat and speed? b) How many had only variable speed?
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Example : A survey of 50 students was conducted regarding whether or not each likes math, science, or English. The following results were
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Math 141 Ch 6 Part 2 - The Number of Elements in a Finite...

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