# hmk2sol - COT 3100 Section 2 Homework#2 Fall 2000 Solutions...

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COT 3100 Section 2 Homework #2 Fall 2000 Solutions 1) a) {0,1,4,16} b) {1,4,16} c) {-12,-6,0} 2) a) 2 7 . This is the exact same question as asking how many subsets of the set {2,4,6,8,10,12,14} there are, since you are forced to pick all the odd numbers every time. b) 8 C 3 *2 7 . Since you are choosing the odd numbers and the even numbers independently to form a cartesian product, you multiply. You can choose 3 odd numbers in 8 C 3 ways. (In part a we determined the total number of ways of picking the even numbers.) c) 8 C 3 * 7 C 5 . Same principle as question b, but this time you must pick exactly 5 even numbers which can be done in 7 C 5 ways. d) 2 14 . This is just like counting the total number of subsets of the set {2,3,4,. ..,15}. e) 10. The subsets are ,{1},{2},{3},{4},{5},{1,2},{1,3},{1,4}, and {2,3}. f) 2 13 – 1. Since you can’t have 7 or 14 in the sets, you basically have to choose non- empty subsets from the set {1,2,3,4,5,6,8,9,10,11,12,13,15}. There are 2 13 subsets of that set and we must subtract out the empty set. If we interpret the question differently, such that we count the set {2,3,7}, for example, because it doesn’t have 14, then our answer is (2 15 – 1) – 2 13 . To see this, basically, the only non- empty subsets we don’t want to count are those with BOTH 7 and 14 in them. So,

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hmk2sol - COT 3100 Section 2 Homework#2 Fall 2000 Solutions...

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