A student asks: > For Pg. 47 #6, the way I translated some of the quantifications in English > sounded kind of awkward, so I used DeMorgan's Law, and as a result, wrote the > exact same thing for [some of the propositions that are logically > equivalent to some of the others]. > Is that correct? Do I have to explain how I used DeMorgan's Law and show some > work before writing down my final "translation"? The intent of the problem is for you to express the propositions in English *as they are*. But if you can *prove* that two of them are logically equivalent and include that proof, then you can express them the same way in English. > > For Pg. 47 #10e, I used three "there exists" symbols, with conjunctions between > them. Is that normal? > Do I need parentheses for each of the three parts? If you mean that you wrote something like: Ex ^ Ey ^ Ez then no, that's not correct. You can, however, write things like: ExEyEz(p ^ q ^ r) However, those are what the book calls "nested quantifiers", which aren't introduced till a later section, so this problem can--and should--be solved without them. > > For Pg. 47 #12, do I have to show work and explain why I think a statement is > true or false? If you don't show your work and get the wrong answer, then you won't get partial credit. > > For Pg. 59 #12, do I need to come up with letters for "exactly one student" and > "Everyone except one student"? For part j, I came up with some huge messy > thing... Maybe that's what I get from doing my homework before the material is > being taught in lecture. Yup! Be patient! > Reading the textbook was kind of vague. I got this: > (Upside down A)x(I(x)->(Backward E)y(C(x,y)^(x(Not equal sign)y))) > Is this even close to being correct? Is the -> symbol used correctly? Do I need > the "x does not equal to y" part? The problem specifically says at least one > OTHER student (i.e. not him/herself). Ax[I(x) -> Ey[C(x,y) ^ -(x = y)]] says: For all x, if x has an Internet connection, then there exists a y such that x and y have chatted over the Internet and x is not the same as y. If you think that that expresses 12j, then it's OK; otherwise, not :-) > > Why is ! used as the symbol for uniqueness? It's quite confusing, since certain > programming languages use it as a "not" symbol. I haven't yet introduced this in class, but the "!" for uniqueness is a much older use than the "!" for negation in programming languages. > > Is it too late to switch recitations? I signed up for the Tues 8AM recitation > because the other two both conflicted with my schedule, but since I had a > schedule change and cleared the Wednesday spot, is it too late to switch? Yes, it's too late, but, as I have said in lecture, if it's OK with your TA for you to sit in on a different section, then you don't have to officially switch, but if the classrooms get too crowded, then you can't.