Exercise 27 Page 457

We are asked to state the law of logic that is illustrated in this exercise. Let's start by analyzing the first statement. &If x>12, &then x+9>20. We can see that this is a conditional statement. We can identify the hypothesis p and the conclusion q in this statement. &If x>12, &then x+9>20. Now we will make sure that the conditional statement is true by solving for x the second inequality.

Since the inequality is true when x>11, we know that the conditional statement must be true. Next, let's recall the Law of Detachment.

In this exercise, the second sentence of the statement, the value of x is 14, means that the hypothesis of our conditional statement is true since 14>12. Using the Law of Detachment we can say that the third sentence — our conclusion — is true. Therefore, the exercise illustrates the Law of Detachment.