My Math Forum MthLogic - Can u help me find out where I made the mistakes?

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 October 16th, 2013, 08:09 PM #1 Member   Joined: Sep 2013 Posts: 43 Thanks: 0 MthLogic - Can u help me find out where I made the mistakes? I'm really trying to understand these things... Consider the domain D = fall CSC courses and all MAT courses, and the predicate symbols C(x): "x is a CSC course", M(x): "x is a MAT course", and P(x; y): "course x is a prerequisite for course y". Using only these symbols (in addition to appropriate connectives and quanti ers), give a clear symbolic statement that corresponds to each given English sentence. Quanti ers may only be over the domain D. Part (a) CSC108 is a prerequisite for CSC148. ? x ? D, ? y ? D, C(x) ? C(y) ? P(x; y) Part (b) There is no prerequisite for CSC104. ? x ? D, ? y ? D, C(y) ? ¬P(x; y) Part (c) Every course has a prerequisite. ? x ? D, ? y ? D, P(x; y) Part (d) No course is a prerequisite for itself. ? x ? D, ¬P(x; x) Part (e) Some CSC course has a prerequisite. ? x ? D, ? y ? D, C(y) ? P(x; y) Part (f) Every MAT course has a prerequisite. ? x ? D, ? y ? D, M(y) ? P(x; y) Could you tell me where I made the mistakes? And how would they look if they were expressed correctly?
October 16th, 2013, 11:35 PM   #2
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Re: MthLogic - Can u help me find out where I made the mista

Quote:
 Originally Posted by danoc93 Part (a) CSC108 is a prerequisite for CSC148. ? x ? D, ? y ? D, C(x) ? C(y) ? P(x; y)
This looks correct.

Quote:
 Part (b) There is no prerequisite for CSC104. ? x ? D, ? y ? D, C(y) ? ¬P(x; y)
This is the wrong way round. What this says is: for every course (x), there is a CSC course (y - may depend on x) for which x is not a prerequisite. What you want is:

? x ? D, ? y ? D, C(x) ? ¬P(y; x)

Quote:
 Part (c) Every course has a prerequisite. ? x ? D, ? y ? D, P(x; y)
This says that there exists a course (x) which is a prerequiste for every course. This should be:

? y ? D, ? x ? D, P(x; y)

Quote:
 Part (d) No course is a prerequisite for itself. ? x ? D, ¬P(x; x)
Correct

Quote:
 Part (e) Some CSC course has a prerequisite. ? x ? D, ? y ? D, C(y) ? P(x; y)
You have to be careful with the order of the qualifiers. This says: there exists a course (x) which is the prerequisite for a CSC course (y). This may be logically equivalent to what you want, but in general it's a mistake to swap the order. The clue is in the question: "some CSC course". So, you want to start with that. So, better is:

? y ? D, ? x ? D, C(y) ? P(x; y)

Quote:
 Part (f) Every MAT course has a prerequisite. ? x ? D, ? y ? D, M(y) ? P(x; y)
Again, the statement starts "every MAT course ...", so you want to start with this:

? y ? D, ? x ? D, M(y) ? P(x; y)

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