Recall from Section 0.1 that the converse of an implication P ⇒ Q is Q ⇒ P. and the con-trapositive is not Q ⇒ not P. In Problems 1-8, give the converse and the contrapositive of the given statement. Which, among the original statement, its converse, and its contrapositive, are always true?
1. If x > 0, then x2 > 0.
2. If x2 > 0, then x > 0.
3. If f is differentiable at c, then f is continuous at c.
4. If f is continuous at c, then f is differentiable at c.
5. If f is right continuous at c. then f is continuous at c.