Form the logical negation of each claim. Try to embed the word \"not\" as deeply

Question

Form the logical negation of each claim. Try to embed the word "not" as deeply into the resulting sentence as possible (or avoid using it altogether).

(a) For all real numbers satisfying a < b, there exists an N Element N such that a+1/n < b.

(b) Given any real number x Element R, there exists n Element N satisfying n > x.

(c) Between two distinct real numbers, there is a rational number.

(d) For all natural numbers n Element N, sqrt(n) is either a rational number or an irrational number.

Explanation / Answer

a) There exists a real number satisfying a

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