Assignment Week 1  Sets and Functions
Please submit using the Fire system
Assignments
(1.) Imagine two sets A and B that satisfy the following properties:
 A U B = {1, 2, 4, 5, 6, 7}
 A ∩ B = {2, 5}
 A \ B = {1, 4, 7}
(a.) Please find two sets A and B that satisfy all of the above properties (at the same time).
(b.) Is your solution the only solution? Explain.

(2.) Find a function
f : ℤ > ℕ
from the integers ("heltal") to the natural numbers, that is surjective but not injective.
Explain why your function is surjective. Explain why it is not injective.
Note: In a previous version of this assignment, the above sentence had a mistake, which is now fixed.
Note: This is not the same assignment as one of the exercises from week 1; this time the function takes integers ("heltal") as arguments, not natural numbers.

(3.) Take a look at the operator #, defined as follows:
# : ℤ x ℤ > ℤ
x # y = x + 3y
(a.) Is the operator # commutative? Explain.
(b.) Is the operator # associative? Explain.
(c.) Does the operator # have an identity e? Explain.
(d.) Can you find two integers a and b that commute ("kommuterar") for #? Explain.

Submission
Submission of this assignment should be done electronically through the Fire system.
The submission deadline is Wednesday, September 9, at 13:00. At this time, you should have submitted a serious attempt to solve the assignment. A serious attempt is either an answer you believe to be correct, or a partial answer plus a detailed explanation of what you have tried to come up with a full answer. An empty document is not a serious attempt.
After submitting, you have until September 21 (midnight) to submit a completely correct version.
You can submit your answers in any of the following formats:
If you submit multiple files, please name and/or number them such that the order in which we should read them is obvious. You can also write a text file, and have it refer to pictures that you upload separately.
