Let D(x, y) be the predicate defined on natural numbers x and y as follows: D(x,...

Let D(x, y) be the predicate defined on natural numbers x and y as follows: D(x, y) is true whenever y divides x, otherwise it is false. Additionally, D(x, 0) is false no matter what x is (since dividing by zero is a no-no!). Let P(x) be the predicate defined on natural numbers that is true if and only if x is a prime number. 1. Write P(x) as a predicate formula involving quantifiers, logical connectives, and the predicate D(x, y). Assume the domain to be natural numbers.

Hint 1: n is prime if and only if the only numbers that divide it are 1 and n.

Hint 2: You might have to use conditionals.

2. Consider the proposition “There are infinitely many prime numbers”. Express the proposition as a predicate formula using quantifiers, logical connectives and the predicate P(x). Assume the domain to be natural numbers. Note that you don’t need to use the answer from the previous part in this problem; you can write your answer in terms of P(x).

3. Write the negation of the predicate formula obtained in part 2. Make sure you take the negation all the way in so that it sits right next to P(x) in the final expression.

Only want to know what the answer for 3 should be

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Expert Solution

Colby Messinger answered 1 year ago

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