Discrete math questions. thank you! Translate the following into first order log

Question

Discrete math questions. thank you!

Translate the following into first order logic. Let P(x) : x is prime, E(x) : x is even

1. There are at least two prime numbers

What I've got is Answer from the book is

(x){P(x)^(x)}{P(y) -> (xy)} (x)(y) {p(x)^ p(y) ^ xy}

I know there can be multiple answer, but I'm not sure mine is correct or not. and also don't know how to get the answer (x)(y) {p(x)^ p(y) ^ xy} could you tell me?

2. There is a smallest prime number

what I have got is

(x){P(x)^(x)}{P(y) -> (x>=y)} I don't have a answer for this and I'm not sure my answer is correct or not. could you check this for me ? thank you very much

Explanation / Answer

1. The answer from the book (x)(y) {p(x)^ p(y) ^ xy} is correct.

Your answer (x){P(x)^(x)}{P(y) -> (xy)}

which has a mistake and should be

(x){P(x)^(y)}{P(y) -> (xy)}

is incorrect.

It translates to:

There exists a prime number and any other prime number is not equal to it.

2. Your answer has two mistakes and is written in corrected form as

(x){P(x)^(y)}{P(y) -> (x<y)}

x should be the smallest prime number and hence x < y.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.