Which element is not in f 1101 animation captions 1 a

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 set doe
not 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 the
second 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 with
f({a,b,c}) = 111.
4. f de±nes a bijection between the set {0,1}
3
and the power set of {a, b, c}. Therefore
| P ( X ) | = | {0, 1}
3
| .
1
2 n
1 2 n
i i i
-1
i i i
n
-1
4
Check
Show answer
©zyBooks 05/12/18 13:48 263732
Anjaney Mahajan
NCSUCSC226ScafuroSpring2018
©zyBooks 05/12/18 13:48 263732
Anjaney Mahajan
NCSUCSC226ScafuroSpring2018
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3) How many elements are in the set f
(0000)?
1
The k-to-1 rule
A group of kids at a slumber party all leave their shoes in a big pile at the door. One way to count
the number of kids at the party is to count the number of shoes and divide by 2. Of course, it is
important to establish that each kid has exactly one pair of shoes in the pile. Counting kids by
counting shoes and dividing by 2 is an example of the k-to-1 rule with k = 2. Applying the k-to-1
rule requires a well de±ned function from objects we can count to objects we would like to
count. In the example with the shoes, the function maps each shoe to the kid who owns it. Here
is 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:X → Y is a k-to-1 correspondence if for every y ∈ Y, there are
exactly k different x ∈ X such that f(x) = y.
A 1-to-1 correspondence is another term for a bijection, so a bijection is a k-to-1 correspondence
with k = 1. The k-to-1 rule uses a k-to-1 correspondence to count the number of elements in the
range 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.
PARTICIPATION
ACTIVITY
10.2.3: An example of the k-to-1 rule.
PARTICIPATION
ACTIVITY
10.2.4: K-to-1 rule.
-
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Animation 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 263732
Anjaney Mahajan
NCSUCSC226ScafuroSpring2018
©zyBooks 05/12/18 13:48 263732
Anjaney Mahajan
NCSUCSC226ScafuroSpring2018

5/12/2018 zyBooks
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