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Homework Help: Making an existentially-quanified statement to define composite number and prime

  1. Jun 4, 2010 #1
    Sorry if I'm writing on wrong board.

    1. The problem statement, all variables and given/known data

    1) Write an existentially quantified statement to express conditions for composite number ( composite number m is greater than 1 and there is a natural number greater than besides 1 and m, that divides m)
    2) Writing definition using symbolic notation for prime numbers? (p is greater than 1, only natural numbers greater than 0 thatt divides p are 1 and p)

    2. Relevant equations

    3. The attempt at a solution
    ∃ m ∈ ℕ, m ∣ n => 1<m<n
    for the composite

    ∀ a,b ∈ ℕ: a/b=p ∧ a=p ∧ b=1
    for the prime

    I'm 100% sure I'm doing something wrong.. Can anyone help me?
  2. jcsd
  3. Jun 4, 2010 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    If m does not divide n, your statement always holds so every number ends up being composite. You shouldn't be using implications to do this. Try something like
    ∃ m ∈ ℕ, (_____ and _____)

    where you fill in the blanks

    Why is a/b=p here? Primes aren't defined based on what divides to get them
  4. Jun 4, 2010 #3
    Ok. thanks for the advice. How does this look?

    ∃ m ∈ ℕ, m∣n ∧ 1<m<n
    for the composite

    ∀ n ∈ ℕ: n∣p ⇔ n=1 ∧ n=p
    for the prime
  5. Jun 4, 2010 #4
    It looks good to me.
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