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Math Help - Need help with, Determinging sets and truth values

  1. #1
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    Smile Need help with, Determinging sets and truth values

    Hi I am new to the site, I have been doing some examples out of the book and I found these 2 the most difficult for me to understand. My in class notes really didnt help and the book is kind of confusing. Any help would be nice and I would really appreciate it.

    Ex. 2.3 P(m. n) is equivalent m divides n, both variables are the set of positive integers. i have to find the truth values for each of these
    P(4,5)
    P(2,4)
    ∀m∀n P(m, n)
    ∃m∀n P m, n
    ∃n∀mP m, n
    ∀n(P(1, n)
    Ex 1.6 E = set of even integers, O = the set of odd integers. ℤ = the set of all integers. I have to determine the sets
    E ∪ O
    E ∩ O
    ℤ − E
    ℤ − O


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  2. #2
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    Re: Need help with, Determinging sets and truth values

    does 4 divide 5? that is, is there some positive INTEGER k with 4k = 5? (i suggest checking integers in the range of 1 to 2).

    does 2 divde 4? is there some positive integer k with 2k = 4?

    does every positive integer divide every positive integer?

    does some positive integer divide every positive integer? (this isn't that hard....)

    is there some positive integer that is divisible by ALL positive integers? (how big would this integer have to be?)

    is P(1,n) true for all n? (that is: does 1 divide n, no matter what n is?)

    can you think of another name for "all even and odd integers"? (hint: an integer is either:____ or ____).

    is any integer both even AND odd (this is what "intersection" means in logical terms)?

    what do you have left if "you take out all the even integers out of the integers"? (this is what Z - E means).
    Thanks from HallsofIvy
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