1.Given compound statement: " > 0, > 0, 0 < < |() | ." Write its following related statements.

The negation:

The contrapositive:

The Converse

The Inverse

2.Prove or disprove each statement by the indicated method. (1). Direct Proof (use definition(s) only): ", , if and are odd, then + + is odd."

(2). A Counterexample: " sets and , ( ) = () ()." ((): the power set of )

(3). Contraposition: "m, n Z with 3|m, 3 (m + n) 3 n."

(4). Contradiction: " x, y, z R, if all x + y, y + z, z + x Q,then all x, y, z Q."

(R: set of real numbers; Q: set of rational numbers)