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Math Help - Nested Quantifiers

  1. #1
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    Nested Quantifiers

    need help with this


    Use (nested) quantifiers and predicates to express the following statements.

    a) “There is someone in class who on every day of 2007 drank coke.”

    b) “There isn't any person in the room who has visited every capital city in world.”

    c) “For each real number, there is another number which is its additive inverse.”
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  2. #2
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    Quote Originally Posted by smartguy View Post
    need help with this


    Use (nested) quantifiers and predicates to express the following statements.

    a) “There is someone in class who on every day of 2007 drank coke.”

    b) “There isn't any person in the room who has visited every capital city in world.”

    c) “For each real number, there is another number which is its additive inverse.”
    As i said in another thread a good book with a lot of examples in formalizing every day sentences is: Logic by schaum's outline series

    Problem (c) in your question is a classic formalization of the additive inverse in real Nos

    Here formalization can be done in two ways:

    1) If you mention the set in which you state your axioms and definitions,which in this case in concern is the set of real Nos,then we have:

    \forall x\exists y. x+y=0

    2) if you do not define the set then you can include it in your formalization in the following way:

    \forall . x\in R\rightarrow\exists y (y\in R\wedge x+y=0)

    YOU can do the rest of the problems
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