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CMSC 250 Quiz #3 Monday, Sept. 24, 2001

Write all answers legibly in the space provided. The number of points possible for each question is indicated in square brackets - the total number of points on the quiz is 30, and you will have exactly 15 minutes to complete this quiz. You may not use calculators, textbooks or any other aids during this quiz.
  1. [16 pnts.] For each of the following English Sentences, translate the meaning into formal notation using the symbols ($\exists$, $\forall$, $\wedge $, $\vee $, $\sim $, and $\rightarrow$). On the next line write the negation of the original statement using formal notation.

    There is a tree taller than any building.
    Domains: all buildings and all trees
    Predicate: T(x,y) = x is taller than y
    statement:
     
    negation:
     
     
    The square of any even integer is an even integer.
    Domain: all integers
    Predicates: E(x) = x is even
    statement:
     
    negation:
     
     
    No pigs have wings.
    Domain: all pigs
    Predicate: W(x) = x has wings
    statement:
     
    negation:
     
     
    There are at least two people here.
    Domain: all people
    Predicate: H(x) = x is here
    statement:
     
    negation:
     
     

    $\downarrow$ TURN OVER $\downarrow$

  2. [7 pnts.] Express the negation of the propositon $p$:

    $\forall n \in N$ $\exists y \in N$ such that $y > n$
    Use neither the negation symbol ($\sim $) nor the word ``not''.




















  3. [7 pnts.] Give an example of a predicate P(x,y) where the (Domain of x = Domain of y = Z (integers)) so that it is true that

    \begin{displaymath} \forall x \exists y \,\,\,\,\,\, P(x,y) \end{displaymath}

    but false that

    \begin{displaymath} \exists y \forall x \,\,\,\,\,\, P(x,y) \end{displaymath}

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John Arras
2001-10-10