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Math Help - Logical Formulae

  1. #1
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    Exclamation Logical Formulae

    Hey,

    I can't do a question and need help ugently, i have been asked to write;

    "The Set A has at most 2 elements"

    as a Logical Formulae. But have no idea how to go about it.

    Thanks

    D
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dagreenhill View Post
    Hey,

    I can't do a question and need help ugently, i have been asked to write;

    "The Set A has at most 2 elements"

    as a Logical Formulae. But have no idea how to go about it.

    Thanks

    D

     <br />
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)<br />
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  3. #3
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    Thumbs up blah

    Quote Originally Posted by CaptainBlack View Post
     <br />
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)<br />
    Thanks!
    but..

    Is There a less specific way of writing that? A general formula or something? maybe containing "for all"? Or mentioning the empty set? since it is "at most"
    Last edited by dagreenhill; August 13th 2008 at 02:38 AM. Reason: additional information
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  4. #4
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    Quote Originally Posted by dagreenhill View Post
    Thanks!
    but..

    Is There a less specific way of writing that? A general formula or something? maybe containing "for all"? Or mentioning the empty set? since it is "at most"
    Since you ask for a formula involving quantification, this is how I'd write it and how you would probably see it written
    in most any textbook on axiomatic set theory. As you can see, there's no need for explicit mention of the empty set.
    The key here is to recognize that it's a hypothetical statement.

    (Note: 'e' denotes set membership; the other symbols should be obvious).

    (x)(y)(z) [[(xeA ^ yeA) ^ ~(x = y)] -> [zeA -> [(z = x) V (z = y)]]]
    Last edited by PiperAlpha167; August 14th 2008 at 10:57 PM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
     <br />
a, b,c \in A \Rightarrow (a=b) \vee (a=c) \vee (b=c)<br />
    (a,b,c) \in A \times A \times A \Rightarrow (a=b) \vee (a=c) \vee (b=c)

    RonL
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