CISC 203 Problem Set 1
January 12, 2024
1. Put your answer to Question 1 here. Note: Remove irrelevant content/text from the template to not lose the formatting mark(s).
2. Note: Remove irrelevant content/text from the template to not lose the formatting mark(s).
(a) If Question 2(a) exists, you may enter it like this. Make sure it’s correct!
(b) Put your answer to Question 2(b) here, if it exists. 2(b) or not 2(b)?
3. Put your answer to Question 3 here. Check out the sample equation below with a numerical label.
This is an inline equation: x = 2/1.
Here is the same equation again:
Maybe instead you want some math inline with your text. Well, here you go: For multisets, use: Again, please remove irrelevant content/text from the template to not lose the formatting mark(s).
4. Put your answer to Question 4 here. Note: Hand-written solutions to any question that are scanned/embedded as an image will not be accepted. But we are showing you how to embed images just for assignments where diagrams are required.
Don’t forget to remove this sample material from your submission.
5. Put your answer to Question 5 here.
6. Put your answer to Question 6 here.
More equation samples, by request:
A ∪ B = C (6)
7. A LaTeX table example:
8. A few sample TikZ pictures, to help with drawing graphs/diagrams in LATEX:
9. Prove (A ∪ B)C = AC ∩ BC..
10. For A = {a ∈ R : |a| ≤ 2} and B = {b ∈ R : |b| = 2}.
11. Let n ∈ N and n > 0, and let the set An = {x ∈ R : −n/1 ≤ x ≤ n/1}.
Find and .
12. Let R be the relation defined on the set Z by a R b if 3 | (a 2 − b 2 ). Note that 3 | mn implies that 3 must divide either m or n or both.
13. Give a combinatorial proof (an algebraic proof will not be accepted: see Module 1, Proposition 15 and Module 3, Theorem 3 for two examples of combinatorial proofs) that
14. Let a = 34 and b = 55. Use Euclid’s algorithm to find gcd(a, b) and to find integers m and n such that gcd(a, b) = am + bn.
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