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Truth Value Of Statements

  1. Sep 18, 2012 #1
    The question is, "Determine the truth value of each of these statements if the domain consists of all integers?"

    The statements are:

    [itex]\forall n(n^2 \geq 0)[/itex]

    [itex]\exists n(n^2=2)[/itex]

    [itex]\forall n(n^2\geq n)[/itex]

    [itex]\exists n(n^2 less than 0) [/itex]

    Does it seem, from reading the question, that I am to determine the truth value of the statement by simply looking at it, or is there some proving process involved?
     
  2. jcsd
  3. Sep 18, 2012 #2

    jbunniii

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    If you can determine the truth by simply looking at it, that seems fine to me. If this is homework, you may want to write a brief explanation even if you could see that it was true by inspection. For example, for the first statement you might write "this square of any real number is ______, therefore this statement is _______"
     
  4. Sep 18, 2012 #3
    What if I was to prove them? How would I go about that? Any hints? Would negating each statement be a good start?
     
  5. Sep 18, 2012 #4

    jbunniii

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    Negation might be useful for some of these. Others will probably be more straightforward to prove directly.

    For example, to prove that [itex]n^2 \geq 0[/itex] is true for all integers [itex]n[/itex], try considering the following three cases separately: [itex]n > 0[/itex], [itex]n = 0[/itex], [itex]n < 0[/itex].
     
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