Discrete Mathematics for Computer Scientists -- Assignment Week 1DIT980, HT 2015
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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.