Provide either a proof or a counterexample for each of these statements.(a) For all

Chapter 1, Problem 4

(choose chapter or problem)

Provide either a proof or a counterexample for each of these statements.(a) For all positive integers x, is a prime.(b) (Universe of all reals)(c) (Universe of all reals)(d) For integers a, b, c, if a divides bc, then either a divides b or a divides c.(e) For integers a, b, c, and d, if a divides and a divides then adivides(f) For all positive real numbers x,(g) For all positive real numbers x, (h) For every positive real number x, there is a positive real number y lessthan x with the property that for all positive real numbers z, (i) For every positive real number x, there is a positive real number y withthe property that if then for all positive real numbers z,