(70 points) Are the following statements true or false? If true, prove it and explain which method(s) of proof you have used; if false, disprove it. d. There exist a pair of consecutive integers such that one of these integers is a perfect square and the other is a perfect cube. e. For any integer n, if n is a perfect square, then n+2 is not a perfect square. f. Between every rational number and every irrational number, there exists an irrational number. g. For any two rational numbers, m and n,mn (i.e., m to the power of n ) is also a rational number