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Math Help - Predicates and Notation of logic..

  1. #1
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    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?

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    Re: Predicates and Notation of logic..

    Quote Originally Posted by NotaClue View Post
    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?
    Click image for larger version. 

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    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?
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  3. #3
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    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
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    Re: Predicates and Notation of logic..

    is this right for I?

    (ALL Symbol) s [studies (s, COM137) ^ ptime(s)]
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    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) ]
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    Re: Predicates and Notation of logic..

    Quote Originally Posted by NotaClue View Post
    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.
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  7. #7
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    Re: Predicates and Notation of logic..

    Quote Originally Posted by Plato View Post
    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?
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  8. #8
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    Re: Predicates and Notation of logic..

    Quote Originally Posted by NotaClue View Post
    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.
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