This homework provides practice in
- applying rules of inference
- the use of quantifiers
- writing precise and correct proofs
- proof techniques
- properties of relations
- equivalence relations and their representations
- the matrix representation of equivalence relations
- partial orders
- properties of partial orders
- the Hasse diagram representation of partial orders
- proving the validity of arguments
- proving mathematical statements
- proving the properties of relations
Solutions to homework questions will be graded not so much on their correctness as on the correct and precise specification of all the steps involved. The rigor of the supporting arguments carry more weight than the correctness of the answer.
Feedback from the previous set of students who attempted this assignment is summarized in the accompanying file, feedback.md.
Based on it, question order within each part has been revised and a question has been rephrased.
Submission is in 2 parts and you have to complete both of them. Not submitting any of them will result in a loss of marks. Both are due simultaneously. Please make sure to submit well in time. There is no late submission. Please talk to your instructor in advance if you are at risk of missing the deadline.
Write your solutions in the same LaTeX file, hw3.tex, as provided and push the completed file to your team's repository. The files in the repository at the time of the deadline will be taken as your team's submission. Make sure that any included files, e.g. image files, are present in the repository. Files that do not compile cannot be graded. So it is best to work with a local installation of LaTeX and use VS Code for collaboration with your buddy.
This is a team submission, i.e. a single submission per team. Your team has a single repository to which each of you will have access. Your team submission will be assigned a Submission Score based on the correctness of the contained solutions.
Deadline: 2359h on Mon, 4 Apr
Fill out the feedback form that will be made available under the Assignments module on the course page on Canvas.
This is an individual submission, i.e. each of you has to fill the form. Filling the form contributes to your Team Factor which is 1 by default and is penalized in case of non-submission of the form, misreporting feedback, or unequal contribution to the submission as reported by your buddies and/or the commit history on GitHub.
Deadline: 2359h on Mon, 4 Apr
Your score in the assignment is the product of your Submission Score and Team Factor.
It is okay to consult and use outside resources as long as they are duly cited in your submission. Not mentioning them will be seen as a case of passing outside work as your own which is a case of academic dishonesty.
In case of confusion or lack of clarity, do not hesitate to reach out to the course staff. We also encourage you to
- discuss with your buddy,
- post in the homework discussion thread.
There is a lot to take in and it is natural to get confused. Do not feel shy to reach out for help or clarification in a timely manner.