4 votes 4 votes 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? $(\forall m) (\exists n) (n > m) \text{ implies Prime}(n)$ $(\exists n) (\forall m) (n > m) \text{ implies Prime}(n)$ $(\forall m) (\exists n) (n > m) \wedge \text{Prime}(n)$ $(\exists n) (\forall m) (n > m) \wedge \text{Prime}(n)$ Mathematical Logic cmi2010 first-order-logic + – go_editor asked May 19, 2016 edited Nov 8, 2019 by go_editor go_editor 837 views answer comment Share Follow See 1 comment See all 1 1 comment reply Prashant. commented Jul 6, 2017 reply Follow Share Debashish Deka , Bikram explain each option what I am getting is not close to what question asking. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 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 indranil21 answered Sep 12, 2020 indranil21 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Ans B) i.e. among all natural numbers which are prime are range greater than other range of natural number srestha answered May 19, 2016 srestha comment Share Follow See all 4 Comments See all 4 4 Comments reply Mk Utkarsh commented Apr 30, 2018 reply Follow Share why not c? 1 votes 1 votes chirudeepnamini commented Jan 14, 2020 i edited by chirudeepnamini Jan 15, 2020 reply Follow Share @srestha I am also getting c Translation of option c: For every natural number n, there is a natural number m which is greater than m and it is a prime. If this is true,one can give me any natural number m, i can give a prime number n which is greater than m. Hence it implies prime numbers are infinite. Translation for other options: Option a: for every natural number m, there is a natural number n and if n is greater than m then n is prime. This is false if we take m=2,n=4. Option B: If there is a natural number n greater than all the natural numbers, then n is a prime. Option d: There is natural number n which is greater than all the natural numbers,and n is prime. 1 votes 1 votes srestha commented Jan 14, 2020 reply Follow Share @chirudeepnamini what is difference between c and d?? 0 votes 0 votes chirudeepnamini commented Jan 15, 2020 i edited by chirudeepnamini Jan 15, 2020 reply Follow Share @srestha option c says that : for every natural number m,there is a natural number n greater than m and n is prime. this n can be less than some other natural number x. for example, for m=1 i can have n=2 , for m=2,n=3,for m=3,i can have n=5, for m=4, i can have, n=5...... But option d says that: There is a natural number n, greater than all the natural numbers and n is prime. this says that, for all values of m=1,m=2,m=3,...... there is a single natural number n greater than every value of m and it is prime(single is not correct word to use) clearly such number can't exist. the words in bold italic makes the difference between option c,d this image might be helpful edit: page number 60 of kenneth rosen 7th edition has image that explains in a better way 0 votes 0 votes Please log in or register to add a comment.