My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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)]
danoc93 is offline  
 
September 30th, 2013, 08:15 PM   #2
Global Moderator
 
CRGreathouse's Avatar
 
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:
Originally Posted by danoc93
? s ? S, ? c ? C, [E(s, c) ? D(s)]
This says:* there is a student that either has a dog or is enrolled in at least one course other than computer science.

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!
CRGreathouse is offline  
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.
danoc93 is offline  
September 30th, 2013, 08:51 PM   #4
Global Moderator
 
CRGreathouse's Avatar
 
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:
Originally Posted by danoc93
I thought => was an implication.
It is. What do you understand an implication to mean?
CRGreathouse is offline  
September 30th, 2013, 09:11 PM   #5
Member
 
Joined: Sep 2013

Posts: 43
Thanks: 0

Re: Is this mathematic logic statement is correct?

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by danoc93
I thought => was an implication.
It is. What do you understand an implication to mean?
Well, I understand the symbol of implication as what it should literally mean: Something implying a consequence

Being a student enrolled in at least one CS course implies owning a dog...
danoc93 is offline  
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!
Pero is offline  
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
danoc93 is offline  
September 30th, 2013, 11:55 PM   #8
Member
 
Joined: Sep 2013

Posts: 43
Thanks: 0

Re: Is this mathematic logic statement is correct?

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by danoc93
? s ? S, ? c ? C, [E(s, c) ? D(s)]
This says:* there is a student that either has a dog or is enrolled in at least one course other than computer science.

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!

I kind of get what u meant by *, I just remembered implication is equivalent to ~p or q
danoc93 is offline  
October 1st, 2013, 10:09 AM   #9
Global Moderator
 
CRGreathouse's Avatar
 
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.
CRGreathouse is offline  
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)]
danoc93 is offline  
Reply

  My Math Forum > College Math Forum > Applied Math

Tags
correct, logic, mathematic, statement



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Which is The Correct Statement (function/set) newyear498 Applied Math 9 April 4th, 2012 06:06 AM
Is this statement correct? NeuroFuzzy Calculus 1 September 29th, 2010 01:14 PM
Logic statement Dontlookback Applied Math 9 March 26th, 2010 11:45 AM
Logic: Quantified Statement problem gascan Applied Math 15 March 17th, 2010 03:17 PM
Logic and subsets; it looks ugly, but can it be correct? random_thinker Applied Math 11 June 27th, 2009 01:11 PM





Copyright © 2019 My Math Forum. All rights reserved.