Predicates and Notation of logic..

• Apr 5th 2013, 07:02 AM
NotaClue
Predicates and Notation of logic..
Suppose the predicates studies and ptime about the University are defined as follows:
studies(s, m) means that student s is currently enrolled on module m and
ptime(s) means that s is a part-time student where s is a student in the set
STUDENTS and m is a module in the set MODULES as defined above.

Using the notation of logic represent each of the following propositions:

(i) All part-time students are enrolled on the module COM137
(ii) Only full-time students are enrolled on the module MT123
(iii) No part-time students are enrolled on the module COM137

Using my table I have to answer these.... Can someone take the time to explain this?

Attachment 27814
• Apr 5th 2013, 07:20 AM
Plato
Re: Predicates and Notation of logic..
Quote:

Originally Posted by NotaClue
Suppose the predicates studies and ptime about the University are defined as follows:
studies(s, m) means that student s is currently enrolled on module m and
ptime(s) means that s is a part-time student where s is a student in the set
STUDENTS and m is a module in the set MODULES as defined above.
Using the notation of logic represent each of the following propositions:

(i) All part-time students are enrolled on the module COM137
(ii) Only full-time students are enrolled on the module MT123
(iii) No part-time students are enrolled on the module COM137
Using my table I have to answer these.... Can someone take the time to explain this?
Attachment 27814

I do not follow what you are to do.
Are you asked to symbolize (i)-(iii)?
For what is the table to be used?

What is the complete set of instructions?
• Apr 5th 2013, 07:31 AM
NotaClue
Re: Predicates and Notation of logic..
Yes I am asked "Using the notation of logic represent each of the following propositions I-III. I have to make sure that my answers correspond with my table
• Apr 5th 2013, 07:36 AM
NotaClue
Re: Predicates and Notation of logic..
is this right for I?

(ALL Symbol) s [studies (s, COM137) ^ ptime(s)]
• Apr 5th 2013, 07:39 AM
NotaClue
Re: Predicates and Notation of logic..
Is this right for II?

¬ ( Exists Symbol s [studies (s, MT123) ^ ptime(s) ] )
All Symbol s [ ¬studies (s, MT123) v ¬ptime(s) ]
All Symbol s [studies (s, MT123) => ¬ptime(s) ]
• Apr 5th 2013, 07:40 AM
Plato
Re: Predicates and Notation of logic..
Quote:

Originally Posted by NotaClue
Yes I am asked "Using the notation of logic represent each of the following propositions I-III. I have to make sure that my answers correspond with my table

i) $(\forall x)[\text{ptime}(x)\to\text{studies}(x,COM137)]$

ii) $(\forall x)[\text{studies}(x,COM123)\to\neg\text{ptime}(x)]$

iii) $(\forall x)[\text{ptime}(x)\to\neg\text{studies}(x,COM137)]$

I am still in the dark as to what the table has to do with it.
• Apr 5th 2013, 07:45 AM
NotaClue
Re: Predicates and Notation of logic..
Quote:

Originally Posted by Plato
i) $(\forall x)[\text{ptime}(x)\to\text{studies}(x,COM137)]$

ii) $(\forall x)[\text{studies}(x,COM123)\to\neg\text{ptime}(x)]$

iii) $(\forall x)[\text{ptime}(x)\to\neg\text{studies}(x,COM137)]$

I am still in the dark as to what the table has to do with it.

hey thanks, I think the table is to do with the next part of the question. stating whether some propositions are true or false. Example ~ptime(Brian) V ptime(Dave)

According to my Table the first is true and the second is false which makes this proposition false?
• Apr 5th 2013, 08:33 AM
emakarov
Re: Predicates and Notation of logic..
Quote:

Originally Posted by NotaClue
I think the table is to do with the next part of the question. stating whether some propositions are true or false. Example ~ptime(Brian) V ptime(Dave)

According to my Table the first is true and the second is false which makes this proposition false?

By the first, do you mean ~ptime(Brian) and by the second, do you mean ptime(Dave)? Doesn't the table say that Dave is part-time? And the disjunction of True and False is True: please review the truth table.