# Which element is not in f 1101 animation captions 1 a

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2)Which element is not in f(1101)?Animation captions:1. A function f is a bijection from the power set of {a, b, c} to the set of 3-bit strings. The setdoenot include a,b, or c. Therefore, f() = 000.2. The set {a} includes a, so the ±rst bit of f({a}) is 1. The set {a} does not include b or c, so thesecond and third bits of f({a}) are 0. f({a}) = 100.3. The value of f can be determined the same way for all the subsets of {a,b,c}, ending withf({a,b,c}) = 111.4. f de±nes a bijection between the set {0,1}3and the power set of {a, b, c}. Therefore|P(X) | = | {0, 1}3| .12n1 2niii-1iiin-14CheckShow answer©zyBooks 05/12/18 13:48 263732Anjaney MahajanNCSUCSC226ScafuroSpring2018©zyBooks 05/12/18 13:48 263732Anjaney MahajanNCSUCSC226ScafuroSpring2018
5/12/2018zyBooks10/793)How many elements are in the set f(0000)?1The k-to-1 ruleA group of kids at a slumber party all leave their shoes in a big pile at the door. One way to countthe number of kids at the party is to count the number of shoes and divide by 2. Of course, it isimportant to establish that each kid has exactly one pair of shoes in the pile. Counting kids bycounting shoes and dividing by 2 is an example of the k-to-1 rule with k = 2. Applying the k-to-1rule requires a well de±ned function from objects we can count to objects we would like tocount. In the example with the shoes, the function maps each shoe to the kid who owns it. Hereis a de±nition of the kind of function that is required:De±nition 10.2.2: k-to-1 correspondence.Let X and Y be ±nite sets. The function f:XY is ak-to-1 correspondenceif for every yY, there areexactly k different xX such that f(x) = y.A 1-to-1 correspondence is another term for a bijection, so a bijection is a k-to-1 correspondencewith k = 1. Thek-to-1 ruleuses a k-to-1 correspondence to count the number of elements in therange by counting the number of elements in the domain and dividing by k.De±nition 10.2.3: k-to-1 rule.Suppose there is a k-to-1 correspondence from a ±nite set A to a ±nite set B. Then |B| = |A|/k.PARTICIPATIONACTIVITY10.2.3: An example of the k-to-1 rule.PARTICIPATIONACTIVITY10.2.4: K-to-1 rule.-CheckShow answerAnimation captions:1. 6 cans of juice per pack. f(c) = p if can c belongs to pack p. f is a 6-to-1 function.2. (# cans of juice)/6 = (# packs of juice).©zyBooks 05/12/18 13:48 263732Anjaney MahajanNCSUCSC226ScafuroSpring2018©zyBooks 05/12/18 13:48 263732Anjaney MahajanNCSUCSC226ScafuroSpring2018
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Term
Spring
Professor
WATKINS
Tags
Natural number, Finite set, Anjaney Mahajan