Exercise 48 Page 449

Let's first identify the hypothesis, p, and the conclusion, q, of our conditional statement. If I rode my bike to school, then I did not walk to school.Examining the second if-then statement, we see that the hypothesis and conclusion have not been exchanged. This means it can neither be the converse q→ p, or the contrapositive, ~ q→~ p. What we do notice is that both the hypothesis and conclusion have been negated. If I did not ride my bike to school then I walked to school This fits the description of the inverse. To represent the statements using symbols, we remember that p is the hypothesis and q is the conclusion. Conditional statement:& p → q Inverse:& ~ p → ~ q