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Let $m$ and $n$ range over natural numbers and let $\text{Prime}(n)$ be true if $n$ is a prime number. Which of the following formulas expresses the fact that the set of prime numbers is infinite?

  1. $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$
  2. $(\exists n) (\forall m) (n > m) \text{ implies Prime}(n)$
  3. $(\forall m) (\exists n) (n > m) \wedge \text{Prime}(n)$
  4. $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$
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2 Answers

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Answer – C.

(∀m)(∃n)(n>m)∧Prime(n)

i.e any m you take from set of Natural no there exists some n such that (n>m) AND n is PRIME
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Ans B)

i.e. among all natural numbers which are prime are range greater than other range of natural number

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