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Math Help - Predicates Help

  1. #1
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    Predicates Help

    We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.


    (a) Express in predicate calculus notation the sentence the sum of two odd integers is even.


    (b) Give the negation of the predicate


    Can any please please help me with this question.
    Thank You

    Sorry if this is in the wrong section im new here
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  2. #2
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    Quote Originally Posted by M.A.T.H View Post
    We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.
    (a) Express in predicate calculus notation the sentence the sum of two odd integers is even.
    (b) Give the negation of the predicate
    Can any please please help me with this question.
    Thank You
    Sorry if this is in the wrong section im new here
    Welcome to the forum.
    This is indeed the correct forum for your question.
    However, we want you to show some effort on your part.
    At least tell us what you do not understand about the question.

    Just posting the question and then waiting for an answer is not the way it works.
    Please rework your post.
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  3. #3
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    Quote Originally Posted by M.A.T.H View Post
    We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.


    (a) Express in predicate calculus notation the sentence the sum of two odd integers is even.


    (b) Give the negation of the predicate


    Can any please please help me with this question.
    Thank You

    Sorry if this is in the wrong section im new here

    Well i dont get what 6a is asking or how to do it, im not asking for the answers just how it would be done?

    And for 6b i had a go but not sure show below (as im new here im not sure how to get all them symbols etc so gna have to type it up)

    Backwords E = E
    Z with extra line in it = Z
    Upside down A = A

    Em is an element of Z|O(2m) = Am is an element of Z such that ¬O(2m)
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  4. #4
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    For part a): \left( {\forall x} \right)\left( {\forall y} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]

    You made a good start on part b): \left( {\forall x} \right)\left[ {\neg O(2x)} \right].

    For negations in general use these two rules.
    \neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]\;\& \,\neg \left( {\exists x} \right)\left[ {P(x)} \right] \equiv \left( {\forall x} \right)\left[ {\neg P(x)} \right]
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  5. #5
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    Hey check your pm please thank you, also how to you know what terms u have to put in to get the upside down A and also how can u edit previous posts i cant seem to find the edit button... (could only find it on this post now)
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  6. #6
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    Quote Originally Posted by M.A.T.H View Post
    Hey check your pm please
    Sorry, but that is not the way I choose to work!
    You post your question here so all can profit from them.
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  7. #7
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    Quote Originally Posted by Plato View Post
    Sorry, but that is not the way I choose to work!
    You post your question here so all can profit from them.
    Ahh ok no problem one second let me just copy paste it from my sentbox lol..

    Quote Originally Posted by M.A.T.H
    Hey i would just like to thank you for your help, i tried to work the question out myself and this is what i got its a little different from yours can you help me with what iv done wrong:

    Quote Originally Posted by Plato View Post
    For part a): \left( {\forall x} \right)\left( {\forall y} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]

    You made a good start on part b): \left( {\forall x} \right)\left[ {\neg O(2x)} \right].

    For negations in general use these two rules.
    \neg \left( {\forall x} \right)\left[ {P(x)} \right] \equiv \left( {\exists x} \right)\left[ {\neg P(x)} \right]\;\& \,\neg \left( {\exists x} \right)\left[ {P(x)} \right] \equiv \left( {\forall x} \right)\left[ {\neg P(x)} \right]
    Above is yours this is what u got:

    a)
    {\forall n} is and element of Z|O(2n) \wedge E(n)

    b)
    {\forall m} is an element Z|O(2m) => E(m)

    Can you tell me what or where im going wrong...Please

    I cant seem to do 6b properly..I have to express the result back in english, and wernt sure how to express your answer...So could u help with that please?

    Thank you
    Last edited by mr fantastic; March 4th 2009 at 03:42 PM. Reason: Merged posts
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  8. #8
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    Frankly I don’t know what to say about you are doing.
    Below is the correct answer for part a) [I did add to clarify domain].
    a): \left( {\forall x \in \mathbb{Z}} \right)\left( {\forall y \in \mathbb{Z}} \right)\left[ {O(x) \wedge O(y)\, \Rightarrow \,E(x + y)} \right]

    You can do the same thing for part b).
    The ‘English’ translation of the negation is:
    “No integer is such that twice the integer is odd.”
    Or “Two times any integer is not odd.”
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