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Math Help - Predicate logic problem

  1. #1
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    Feb 2010
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    Trondheim
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    Predicate logic problem

    Formalizing the following two sentences predicate logically:

    1. Nobody likes warm beer (Let B(x) stand for "x like warm beer")

    2. Everyone likes someone, and someone likes all (Let T (x, y) stand for "x likes y")

    Is this right thinking?
    (¬∃x)B(x)

    ((∀xy)T(x,y))/\((yx∀)T(x,y))

    Im dont know how to put it together mathematically correct.
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  2. #2
    Member
    Joined
    Mar 2009
    Posts
    90
    hi Monika,
    1) I think you're answer is right, although I would write it like this:
    <br />
(\forall x)[\neg B(x)]<br />

    but, what you have written is equivalent:
    <br />
\neg (\exists x)[B(x)]<br />

    2) I think you want:
    <br />
(\forall x)(\exists y)[T(x, y)] \wedge (\exists x)(\forall y)[T(x, y)]<br />
    "For all people there exists at least (or some) person, that they like" and "there exist at least (or some) person, who likes everyone."
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