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Unformatted text preview: have an odd number of elements? Remember that in subsets, order doesnt matter. So the question becomes: How many ways can we choose an odd number of elements from A ? Well, there are ( 10 1 ) ways to choose 1 element, ( 10 3 ) ways to choose 3 elements, ( 10 5 ) ways to choose 5, ( 10 7 ) ways to choose 7, and ( 10 9 ) ways to choose 9. Add these together to get the correct answer. Another way to do it is to say: this is the sum of all the odd subsets of 10. By a corollary Prof. Miller proved in class, the number of odd subsets is equal to the number of even subsets. So the number of odd subsets is just the total number of subsets divided by 2. The total number of subsets of A has cardinality 2 1 0, so the number of odd subsets is 2 1 2 = 2 9 . Either way, you get 512 as your answer. Bonus (1 pt): Who was the leading scorer for the Wisconsin mens basketball team during the NCAA tournament? Correct answer is Alando Tucker. 1...
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This note was uploaded on 08/11/2008 for the course MATH 240 taught by Professor Miller during the Fall '08 term at Wisconsin.
- Fall '08