TMUA 2018 Paper 2 Question 12 P2 · Logic & Quantifiers · 6.5Official · 2018 · Q12
nested-quantifiers negation de-morgan
Consider the following statement: For any positive integer N there is a positive integer K such that N ( K m + 1 ) − 1 is not prime for any positive integer m . Which one of the following is the negation of this statement?
A For any positive integer N there is a positive integer K such that there is a positive integer m for which N ( K m + 1 ) − 1 is prime. B For any positive integer N there is a positive integer K such that there is a positive integer m for which N ( K m + 1 ) − 1 is not prime. C For any positive integer N there is a positive integer K such that for any positive integer m , N ( K m + 1 ) − 1 is not prime. D For any positive integer N , any positive integer K and any positive integer m , N ( K m + 1 ) − 1 is not prime. E There is a positive integer N such that for any positive integer K there is a positive integer m for which N ( K m + 1 ) − 1 is not prime. F There is a positive integer N such that for any positive integer K there is a positive integer m for which N ( K m + 1 ) − 1 is prime. G There is a positive integer N such that for any positive integer K and any positive integer m , N ( K m + 1 ) − 1 is prime. H There is a positive integer N and a positive integer K for which there is no positive integer m for which N ( K m + 1 ) − 1 is prime.
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