# Making an existentially-quanified statement to define composite number and prime

1. Jun 4, 2010

### Iwantttt

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. Jun 4, 2010

### Office_Shredder

Staff Emeritus
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

3. Jun 4, 2010

### Iwantttt

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

4. Jun 4, 2010

### Tedjn

It looks good to me.