Sets

An assignment in CS 303. Some problems are from MCS

Assignment

1. Prove an identity.
   1. Give a proof that the subseteq operator makes a partial order. Namely, prove that the subseteq operator is reflexive, antisymmetric, and transitive. When you need to use names for sets, use A, B, C in the proof. PROOF.
   2. Give a proof that set intersection is associative. When you need to use names for sets, use A, B, C in the proof. PROOF.
2. Basic questions about sets / basic reasoning / using the identities and rules for sets.
   1. MCS Problem 15.4. What is the answer, you should come up with a formula, and explain why.
   2. MCS Problem 15.5. Make sure to only use set notation in part a. In part b, give a formula, also work it out, and explain.
   3. MCS Problem 15.9. Again, give formulas, explain why, work them out. ** most interesting problem.
   4. MCS Problem 15.13. Again, give formulas, explain why, work them out. There are a variety of ways to do this. You might read through the following (and pages it links to): https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)
   5. MCS Problem 15.30. ** tied for most interesting. PROOF. For the definition of multinomial coefficients, see https://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients
   6. MCS Problem 15.35. What is the answer for each, and explain why.