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Math Help - Predicate Logic -- Can you word this expression in English?

  1. #1
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    Predicate Logic -- Can you word this expression in English?

    I'm pretty sure I can solve the other parts of this problem set if you all can just word out this expression for me:

    (x0 > y0 → z = x0) o (x0 <= y0 → z = y0)

    The quantifier in the middle throws off my wording
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  2. #2
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    Quote Originally Posted by angrynapkin View Post
    I'm pretty sure I can solve the other parts of this problem set if you all can just word out this expression for me:
    (x0 > y0 → z = x0) o (x0 <= y0 → z = y0)
    The quantifier in the middle throws off my wording
    I have absolutely no idea how to read that.
    Is this close?
    \left[ {x_0  > y_0  \Rightarrow x_0  = z} \right]~{\color{red}{?}}~\left[ {x_0  \leqslant y_0  \Rightarrow y_0  = z} \right]

    But what in the world does ? stand for?
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  3. #3
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    It's the Universal quantifier. Some schools use the upside down A, we use the ^ symbol as well.
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  4. #4
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    Quote Originally Posted by angrynapkin View Post
    It's the Universal quantifier. Some schools use the upside down A, we use the ^ symbol as well.
    Is this it? \left( {\forall z} \right)\left( {\left[ {x_0  > y_0  \Rightarrow x_0  = z} \right] \wedge \left[ {x_0  \leqslant y_0  \Rightarrow y_0  = z} \right]} \right)
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  5. #5
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    Right. Well that's the symbol at least. I just need to figure out what the function actually does.
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  6. #6
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    Quote Originally Posted by angrynapkin View Post
    Right. Well that's the symbol at least. I just need to figure out what the function actually does.
    That is \max \left\{ {x_0 ,y_0 } \right\}.
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