Exam 1 Review. Your first exam will take place on Thursday, September 26th, and will cover Sections 1.1-2.6. NOTE: If the review sheet does not display properly with the above link, try the Google Doc version.

Exam 2 Review. The second exam will take place on Thursday, October 24th. NOTE: link leads directly to the Google Doc version, let me know if you have any trouble viewing it.

Exam 3 Review. The third exam will take place on Thursday, November 21st. Link leads to the Google Doc.

Final Exam Review. The final exam will take place on Thursday, December 19th. Link leads to the Google Doc. *Solutions will be added within the next few days*.

Thanks for the review. I have a few questions:

6c) (Composite) D Intersect E — I got the answer to be (5,6) instead of the empty set. Doesn’t that little piece of everything but D interest with E?

8d) I understand the union. Basically for UAa, I got = {[3,6],4} x [3,4], which is the horizontal line between x = 3 & x = 6 on the plane at y = 4, all between the y = 3 and y = 4. Ie, [3,6]x[3×4]. I thought the intersection would then be the horizontal line between x=3 and x=6 at y=4, which I interpreted as [3×6]x {4}. But I see the answer is the reverse, {4}x[3,6]. Am I thinking of the graph wrong?

10a) For the truth table, under Q^~P, I got FFTF, when Q is TFTF and ~P is FFTT. Right? I guess this then changes the rest of the truth table.

Thank you!!

Hi Patty,

I’ll take them one at a time – here goes:

6c) YES, the answer is indeed (5,6). I’ve updated the answer key.

8d) Start with the union: First, notice that for any individual alpha, the set A_alpha consists of two vertical lines, one located at x=alpha and the other at x=4, stretching from y=3 to y=4. The union will consist of all vertical lines, at every x location between x=3 and x=6, each line stretching from y=3 to y=4. This means we have included everything in the rectangle stretching from x=3 to x=6, and y=3 to y=4 — that is, the rectangle [3,6]x[3,4]. (NOTE: the one particular vertical line located at x=4 shows up in ALL the sets — it happens to lie in the middle of this rectangle, and gets included just like all the others).

For the intersection, the only thing that each of the sets A_alpha have in common is the single vertical line located at x=4, stretching from y=3 to y=4. Since the x value is the same for each of these vertical lines (x=4), and the y ranges from 3 to 4, for the intersection we get the vertical line {4}x[3,4].

10a) YES, you are quite right – and my truth table had corresponding errors throughout. I believe I’ve fixed it now, but don’t hesitate to check me.

Thanks for the great work – let me know if any of these need further clarification.

– Prof. Reitz

Thank you!!

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