Homework answers / question archive / Think about your answers to the "self-reflection" problems over this year (the ones that start with “How much time did you spend

Think about your answers to the "self-reflection" problems over this year (the ones that start with “How much time did you spend

Sociology

Share With

Think about your answers to the "self-reflection" problems over this year (the ones that start with “How much time did you spend..."). When you wrote down ideas of what you were going to do, did you ac- tually do them? If not, why not? Did you tell the truth to yourself/me when you answered those questions over the semester? Did you lie? Why did you lie? Did you learn anything from thinking about these questions? Why do you think I ask you these questions? (I am only interested in real answers that you took some time to think about. Just say things that feel true to you, and don't worry about making me happy.) 2. You have a crush on a fellow student in Math 42. Prof. Zhang is splitting the class (40 people total, including you) into groups of 5. What's the probability that your group contains the student you have a crush on? (optional: your answer should be fairly simple; see if you can get it in a couple of different ways) 3. For sets A and B, prove that AUB= (A - B) U (B - A) U (ANB). Again, a picture is not a proof (but it helps). Just carefully go through definitions: "what does it mean that x € (A - B)?" etc. 4. Your lawyer tells you: "If people have A3 status then they are eligible for the E4 Visa. Anyone who has A2 status can also apply for the F9 membership. You have A2 status and the E4 Visa, so you have both A2 and A3 status, and thus you have F9 membership as well. People with both A2 and F9 get the A5 status for free, so you have A5 status." All the assumptions the lawyer had about you were correct, but there is a problem with his reasoning. What is it? 5. Let Fo = 0, F1 = 6. For each integer n > 2, let Fn = 2*Fn-1+6*Fn-2, Prove that 4 Fn for all n > 2. 6. How many antisymmetric relations on {1, 2, ...,n} are there? (hint: to do problems like these, do things one at a time. For example, look at (3, 4) and (4,3) – how many ways can these elements be in (or not 1 in) your relation? Can you have both? Neither? Just one? Check your answers with small n!) 7. You and your friends play poker, but with just 3 cards. A flush is still 3 cards of the same suit, and a straight is again 3 cards that are consecutive (A-2-3 and Q-K-A are both allowed). If you draw 3 cards uniformly at random, what is the probability you get a flush? A straight? A straight flush (which is both a straight and a flush)?