"2 is the only even prime number" using quantifiers

Question

if "2 is the only even prime number"

• Prove using quantifiers Let P(x) = x is prime number ∃xP(x)

AND

• Negate the statement that you have ¬∃xP(x)= ∀x(¬P(x))

Is this right?

edited: what about this? ∀n ∈ N(n is even ∧ n is prime ⇒ n=2)

Answer 1

Hint: The statement "2 is the only even prime" becomes, in slightly more formula-friendly language

There does not exist a number which all of the following are true:

• It is even
• It is different from 2
• It is prime