Let D(x, y) be the predicate defined on natural numbers x and yas follows: D(x, y) is true whenever y divides x, otherwise it isfalse. Additionally, D(x, 0) is false no matter what x is (sincedividing by zero is a no-no!). Let P(x) be the predicate defined onnatural numbers that is true if and only if x is a prime number. 1.Write P(x) as a predicate formula involving quantifiers, logicalconnectives, and the predicate D(x, y). Assume the domain to benatural numbers.
Hint 1: n is prime if and only if the only numbers that divideit are 1 and n.
Hint 2: You might have to use conditionals.
2. Consider the proposition “There are infinitely many primenumbers”. Express the proposition as a predicate formula usingquantifiers, logical connectives and the predicate P(x). Assume thedomain to be natural numbers. Note that you don’t need to use theanswer from the previous part in this problem; you can write youranswer in terms of P(x).
3. Write the negation of the predicate formula obtained in part2. Make sure you take the negation all the way in so that it sitsright next to P(x) in the final expression.
Only want to know what the answer for 3 should be
