For each of the following statements state the converse, inverse, and contrapositive. Also determine the truth value for each given statement, as well as the truth values for its converse, inverse, and contrapositive. (Here "divides" means "exactly divides.")
(a) [The universe comprises all positive integers.]
If m > n, then m2 > n2.
(b) [The universe comprises all integers.]
If a > b, then a2 > b2.
(c) [The universe comprises all integers.]
If m divides n and n divides p, then m divides p.
(d) [The universe consists of all real numbers.]
∀x [(x > 3) → (x2 > 9)]
(e) [The universe consists of all real numbers.]
For all real numbers x, if x2 + 4x - 21 > 0, then x > 3 or x < - 7.