Link to the Midterm Exam |
Questions |
General Instructions
- Your statement "The exam is due at 8:30pm on March 4th." suggest to me that you would like the exam handed to you at exactly 8:30pm, no sooner or later.
- It probably does suggest that, but it shouldn't. To be clearer: the exam is due by 8:30pm on March 4th. To be even clearer: assuming you haven't turned the exam in early, which you're certainly welcome to do, you should hand me your exam at either the start of class, or when you arrive. That is to say, I don't really intend to lecture to people who are busy finishing the exam. If you need the time from 5:30 to 8:30 to work on the exam more than you need the lecture, I'm sure you can find somewhere to sit and work.
Question 4
- Your intentions regarding meta-reasoning for this problem are unclear to me, since your explicit definition of the characters is not enough in and of itself to answer the question. For example, you do not say which characters are male versus female, but still ask questions regarding this characteristic.
- True. I never state whether Wednesday is female, but implied in the sentence "Wednesday is their daughter" is the fact that Wednesday is female, and so forth. So even though only one "brother" relationship is explicitly defined, you should use basic real-world knowledge about the way these relationships work to determine the sets. (Including things like "If two people are married, they aren't brother and sister".)
- For (a) and (b) we are drawing from the Universe, but are we drawing from the results of (a) and (b) for C and D or also from the universe?
- All of the sets in (a) through (d) in Question 4 are to be considered in relation to U, the universe given at the top of the page.
- Is it safe to say the following or part of the following?
The use of x in questions (a) and (b) has no relationship with the use of y in question (c), that in fact your choice to use either x or y, in each of these cases is arbitrary.
- Yes. It's something I take for granted as being obvious, as a mathematician, but to be clear:
Variables like "x" and "y" (and for that matter, the "s" in the descriptions of sets K and L in questions 6 and 7) are consistent within a single line or
description, but not outside of that line. So the question 4c, the "y" in "{y | y is male}" is different from the "y" in "{y | y has a child}". The variables are chosen
more or less arbitrarily, so you could substitute "x" for "y" as long as you did so consistently throughout the line, e.g.
{y | y is male} = {x | x is male} = {z | z is male}, etc.
Similarly—and this may have been more confusing, for which I apologize—in Question 2, the second and third bullet points in the description of A are
separate points. So all three instances of "y" in "If x ∈ A, y ∈ S, and the governors of x and y have the same first name, then y ∈ A" all represent the
same individual, but the "y"s in the second line are separate from that.
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