BIOLOGY 1A03 Lecture Notes - Lecture 6: Subset

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BIOLOGY 1A03 Full Course Notes
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BIOLOGY 1A03 Full Course Notes
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Warm up: determine the number of subsets of {1,2,3,4,5,6,7,8} We can generalize this: 2n(a) many subsets of set a. Example: how many subsets of {1,2,3,4} have at least 2 elements: try listing things out -> {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4} - things with 2 things. > {1,2,3}, {1,3,4}, {1,2,4}, {2,3,4} things with 3 things. Therefore 11 subsets: try listing out the opposite, not at least 2 (at most 1, -> {}, {1,}, {2}, {3}, {4} 5 things, the total number of subsets = 24 = 16, so, 16-5= 11. Not less than k = more than k-1. Not more than k = less than k+1. Example: how many 4-digit pins contains at least 2 distinct digits. Note: 1,2,3,4 (4 distinct digits)/ 3,3,2,2 (2 distinct digits)/ 6,1,6,6 (2 distinct digits) Opposite to at least 2 is at most 1. Example: how many subsets of {a,b,c,d,e,f} have at most 4 elements. Opposite to at most 4 is not at least 5.

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