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Test 1 eecs2001-M CSC 2001

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1. Question 1–Sets and functions Let n1, n2, . . . , n9 denote the 9 digits of you Student ID. We also let Σ = {a, b, c, . . . x, y, z} be our standard alphabet of letters. We define the following three subsets of the natural numbers: A = {n1, n2, . . . , n9} B = {n1, n2, n3, n4, n5} C = {n6, n7, n8, n9} And we define one subset of Σ: D = {σ ∈ Σ | σ occurs as a letter in your (first last or middle) name} (a) Spell out all of the above four sets by listing their elements. What are the sizes of the sets A, B, C and D? (b) Does there exist a function f that is one-to-one from A to D? If so define one, if not, explain why not. (c) Does there exist a function g that is onto from A to D? If so define one, if not, explain why not. (d) How many

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Test 1
eecs2001-M
Instructor: Ruth Urner


Advice and instructions
• Please prepare one pdf file of size at most 2MB with your answers to the questions.

• Submit your solution on eclass before Monday, February 1, 1pm.

• Do not communicate with anyone about the exam or course content and the solutions
during the 24h exam period. The questions are individualized and correct answers may
differ from student to student. Do not share your solution with other students.

• Include a statement that you prepared your solutions without consulting anyone on
your submission.

• State your name and student ID clearly readable on all pages of your solution file.

• You may refer to all the material taught so far (textbook, slides and tutorials) and use
all results taught without re-proving them. Just clearly state what you are using.

• As had been announced, I will not answer questions during the exam period.
Understanding the questions is part of the test. If you find something ambiguous,
make an assumption, state it clearly and work with that. In case you suspect there is
a mistake in a question, you may email me. If there is indeed a mistake, I will respond
and also make an announcement on eclass so that everyone has the same information.
If you do not receive a response, assume that there was no mistake.

• In you solution file provide one answer to each question. You need to prove all your
claims. Do not provide multiple alternative answers. If you do, the TA will only
consider the first answer you provide.

• The total number of points in this test is 20.

• I wish you good luck and best of success!




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