How to read this logical statement in English?

Question

Statement: ∀n ∈ Z, [(P(n) ∧¬(n=2)) ⇒ O(n)]

where Z is a set of natural numbers P(n) is the predicate "n is a prime number" O(n) is the predicate "n is an odd number"

I got this, but I don't think it sounds right...

for all n that is in the set of natural numbers, n is a prime number and not the prime number 2 implies n is an odd number

What does this mean?? Sorry for the mega newb question, I'm new to this.

Answer 1

Your grammar is a bit questionable but that is the statement that is desired. The statement says that even integers greater than two can't be prime (namely, they are divisible by 2).

A way of writing the statement more naturally is:

Any natural number that is prime and not two must be odd.

Hope this helps,

Answer 2

Yes, you've got it right, but you could be a little less clumsy by saying: For every natural number n, if $n$ is a prime and not equal to $2$, then $n$ is odd.

Alternatively: Every prime number not equal to 2 is odd.