Prove that(a) for every natural number n, (Hint: Use the fact that anddivide by the

Chapter 1, Problem 6

(choose chapter or problem)

Prove that(a) for every natural number n, (Hint: Use the fact that anddivide by the positive number n.)(b) there is a natural number M such that for all natural numbers (c) for every natural number n, there is a natural number M such that(d) there is a natural number M such that for every natural number n,(e) there is no largest natural number.(f) there is no smallest positive real number. (g) for every real number there is a natural number M such that for allnatural numbers (h) for every real number there is a natural number M such that ifthen(i) there is a natural number K such that whenever r is a realnumber larger than K.(j) there exist integers L and G such that and for every real numberx, if then(k) there exists an odd integer M such that for all real numbers r larger thanM,(l) for every natural number x there is an integer k such that(m) there exist integers and such that and for allreal numbers r and s, if and then(n) for every pair of positive real numbers x and y where there existsa natural number M such that if n is a natural number and then