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 thenumber of its position:Position:1 2 3 4 5 6 7 8Number:b) Let p E Fnc(A, B) be the function that maps the position a E A to the numeric digitbEB that occurs below the value of a in the table created above. Draw the arrow diagram ofyour 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? Whyor 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 afunction p: C → A that is injective. For example if both 1, 2 and 3 all lead to 0, we canchoose to have G go from 0 back to 2 (as the single arrow we selected) and make similarchoices 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 thatelement 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?

Name: J number is 00206553 Let A := {1,2, 3, 4, 5,6, 7, 8} and let B :== {0,
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: 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 thenumber of its position:Position:1 2 3 4 5 6 7 8Number:b) Let p E Fnc(