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September 30th, 2013, 06:58 PM  #1 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Is this mathematic logic statement is correct?
I'm doing some homework and I have no idea if I am doing it correctly. Let C represent the set of all computer science courses and let S represent the set of all students. Define the predicate E(s, c) : “student s is enrolled in computer science course c”. And define the predicate D(s) : “student s owns a dog”. (a) Translate each of the following English statements into symbolic logic form using quantified predicates. i. There is at least one computer science student who owns a dog. (A computer science student is a student who is enrolled in at least one computer science course.) ? s ? S, ? c ? C, [E(s, c) ? D(s)] 
September 30th, 2013, 08:15 PM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Is this mathematic logic statement is correct? Quote:
You want ? s ? S, ? c ? C, [E(s, c) ? D(s)] so that both E(s, c) and D(s) need to be true. * Technically, it doesn't quite say this. Bonus points for discovering why!  
September 30th, 2013, 08:28 PM  #3 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Is this mathematic logic statement is correct?
Why does it say that? I thought => was an implication.

September 30th, 2013, 08:51 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Is this mathematic logic statement is correct? Quote:
 
September 30th, 2013, 09:11 PM  #5  
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Is this mathematic logic statement is correct? Quote:
Being a student enrolled in at least one CS course implies owning a dog...  
September 30th, 2013, 10:28 PM  #6 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: Is this mathematic logic statement is correct?
There's a big difference between "and" and "implies". "And" simply means that something has two characteristics. "Implies" means there is a causual relationship between those things. So, if you weren't allowed on a Computer Science course unless you owned a dog, then: Being on a CS course => owing a dog. Whereas, what you have here is at least one CS student who happens to own a dog. Two very different situations! 
September 30th, 2013, 11:51 PM  #7 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Is this mathematic logic statement is correct?
Oh interesting, so instead of implying the two things I should have used and... Thanks

September 30th, 2013, 11:55 PM  #8  
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Is this mathematic logic statement is correct? Quote:
I kind of get what u meant by *, I just remembered implication is equivalent to ~p or q  
October 1st, 2013, 10:09 AM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Is this mathematic logic statement is correct?
What I meant by the star is that the meaning is not exactly the same as There is a student that either has a dog or is enrolled in at least one course other than computer science. because, in principle, there could be a student with a dog but no courses at all, in which case the original statement would be false but the new one true. But assuming there is at least one course the two are the same. 
October 1st, 2013, 10:59 AM  #10 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Re: Is this mathematic logic statement is correct?
So what does this statement mean? ? s ? S, ? c ? C, [E(s, c) ? ¬D(s)] 

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