Chapter 1.6, Problem 19E

Determine whether each of these arguments is valid. If an argument is correct, what rule of inference is being used? If it is not, what logical error occurs?

a) Ifnis a real number such that $n>1$ , then $n^2>1$ . Suppose that $n^2>1$ . Then $n>1$ .

b) If n is a real number with $n>3$ , then $n^2>9$ . Suppose that $n^2>9$ . Then $n\le 3$ .

c) If n is a real number with $n>2$ , then $n^2>4$ . Suppose that $n^2>4$ . Then $n^2\le 4$ .