b) Let ø € Fnc(A, B) be the function that maps the position a e A to the numeric digit bEB that occurs below the value of a in the table created above. Draw the arrow diagram of your function p.

Algebra & Trigonometry with Analytic Geometry
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ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 15E
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J number is 00206553

Let A := {1,2, 3, 4, 5,6, 7, 8} and let B :== {0,1,2,3, 4, 5, 6, 7,8,9}.
a) Write the numeric digits of your student ID (J-number) in the blank slots beneath the
number of its position:
Position:
1 2 3 4 5 6 7 8
Number:
b) Let p E Fnc(A, B) be the function that maps the position a E A to the numeric digit
bEB that occurs below the value of a in the table created above. Draw the arrow diagram of
your function p.
c) Answer the following about the function ø you created in part (b):
(1) Is ø injective? Why or why not?
(ii) Is ø surjective? Why or why not?
(iii) Based on the sizes of A and B, could someone else's function be surjective? Why
or why not?
Transcribed Image Text:Let A := {1,2, 3, 4, 5,6, 7, 8} and let B :== {0,1,2,3, 4, 5, 6, 7,8,9}. a) Write the numeric digits of your student ID (J-number) in the blank slots beneath the number of its position: Position: 1 2 3 4 5 6 7 8 Number: b) Let p E Fnc(A, B) be the function that maps the position a E A to the numeric digit bEB that occurs below the value of a in the table created above. Draw the arrow diagram of your function p. c) Answer the following about the function ø you created in part (b): (1) Is ø injective? Why or why not? (ii) Is ø surjective? Why or why not? (iii) Based on the sizes of A and B, could someone else's function be surjective? Why or why not?
d) Let C := Im(4). Write out C is roster form:
e) For each member of C choose one of the arrows from o that leads to it and create a
function p: C → A that is injective. For example if both 1, 2 and 3 all lead to 0, we can
choose to have G go from 0 back to 2 (as the single arrow we selected) and make similar
choices for the other elements in the image that have more than one arrow leading to it.
If there is only one arrow then that will be the arrow we will use in reverse for that
element in y. Create the arrow diagram for your choice of y.
(f) Draw the arrow diagram for o • y. What do you observe about this function?
Transcribed Image Text:d) Let C := Im(4). Write out C is roster form: e) For each member of C choose one of the arrows from o that leads to it and create a function p: C → A that is injective. For example if both 1, 2 and 3 all lead to 0, we can choose to have G go from 0 back to 2 (as the single arrow we selected) and make similar choices for the other elements in the image that have more than one arrow leading to it. If there is only one arrow then that will be the arrow we will use in reverse for that element in y. Create the arrow diagram for your choice of y. (f) Draw the arrow diagram for o • y. What do you observe about this function?
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