Chapter 2 - Reasoning and Proof - 2-3 Biconditionals and Definitions - Practice and Problem-Solving Exercises - Page 102: 34

D

D is the only statement that is true and has a true converse. A is true, but the converse is not. The converse is, "If $|x|\gt0$, then $x\gt0$. A counterexample to the converse is -5. B is true, but the converse is not. The converse is, "If $x^2=9$, then $x=3$. A counterexample to the converse is -3. C is not true, because $125^3\ne 5$.