Projectonework#1
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Hello, Regarding this line: (c) (¬A∧¬B∧C)∨(¬A∧¬C)?? I'm afraid that this is not a CNF. The most exterior logical connectives of a CNF should only be conjunctions ("∧") , but your answer uses a disjunction to connect two conjunction formulas, and thus you give a DNF (disjunctive normal form) here. I will find another time to read other parts of your project and add more comments! Best, |
Thank you Karl :) |
peihongx
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@dmcnulty27 Hi Dewbird, I've completed my review of your project!
| (c) C that says that x and y are cousins | ||
| (d) O that says that x is an only child | ||
| (e) T that says that x has exactly two brothers | ||
| ``` |
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I will give an example. (a)
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Karl I cannot get the coding to take in Github. So frustrating
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Karl I cannot get the coding to take in Github. So frustrating
There is no spacing between "$" and symbols next to it. Maybe you could search for "Markdown and Latex"? That is weird because I copy your code and paste to my comments, and then it works!
| Male = {w, x} | ||
| Brother = {w, x} | ||
| Aunt = {y} | ||
| Parent_of = {(z,w), (z,x)} |
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It seems you do not specify the value of "Remi", "Mary", "Frank" and "Donnie". Insetad, you assign a value to "William", "Xaivar", "Eunice", and "Zane". Maybe you can somehow change the latter to the former?
| ```(a) ∃x∀y says something like there is some x such that for all y | ||
| (a) ∀x∃y says for all x there is some y | ||
| (b) ∃x∀y∃z says there is some x such that for all y there is some z such that | ||
| (b) ∀x∃y∀z says for all x there is come y such that for all x |
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| ``` Here is my diagram of the universe: [label](file:///Universe.pub) | ||
| U: {0,1} | ||
| R: {(0,0), (0,1), (1,1)} |
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It seems that your graph satisfy two formulas at the same time. In order to differ between them, maybe you need a graph including 3 distinct points.
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For question 1, I get that a and c are tautologies, and b and c are contingent. It looks like you entered (c) twice, rather than doing (b). For question 2, I either get errors when I type in (b) and (c), or I'm told they're tautologies. I've been told by other people that I can type something to the effect of "This is a tautology, so no CNF form is possible. p∨~p", but I don't really understand why. Question 3 looks pretty good to me. I also included statements of non-identity in my answers, but it makes my answers pretty ugly. For instance, for 3(a) I say ∃x∃y∃z(P(z,y)∧P(z,x)∧¬Fx∧x≠y∧x≠z∧z≠y) This makes it clear we're talking about 3 different people (the parent isn't identical to any of the children, and the brothers aren't identical to each other. You can decide if you think these non-identity statements are important. I don't think Karl is including them. For me, 3(b) is ∃w∃x∃y∃z(P(z,y)∧P(w,z)∧P(w,x)∧Fx∧x≠y∧x≠z∧x≠w∧w≠y∧w≠z∧y≠z) 3(c) is ∃v∃w∃x∃y∃z(P(v,w)∧P(v,z)∧P(w,x)∧P(z,y)∧x≠v∧x≠y∧x≠z∧x≠w∧w≠y∧w≠z∧w≠v∧y≠z∧y≠v∧v≠z) 3(d) is ∃x∃y∀z((P(y,z)∧P(y,x)→z=x)∧y≠z∧y≠x) and 3(e) is ∃v∃w∃x∃y(P(v,x)∧P(v,w)∧¬Fw∧P(v,y)∧¬Fy∧∀z((P(v,z)∧¬Fz)→((z=x)∨(z=w)∨(z=y)))∧v≠w∧v≠x∧v≠y∧v≠z) It looks like you have both your old and new answers to 4 and 5. Besides that, this looks good to me! |
Hopefully, these corrections go to the right place.
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