Quantifiers. For each of the following statements, give a concise English description of the logical formula (for example, "every natural number is the biggest"), and then either prove or disprove the statement.

(a) i N, j N, i < j.

(b) j N, i N, i j.

(c) X N, n X, n 0.

(d) X N, n X, n 0.

(e) X N,(X 6= ) n X, k X, k n