Exercise 53 Page 449

When a conditional statement and its converse are both true, it can be rewritten as a single biconditional statement. If p is the hypothesis and q the conclusion, the biconditional statement is written as p if and only if q. In the exercise we have been given a hypothesis and a conclusion. p:& x^2-10=x+2 q:& x=4 Let's first investigate the truth value of the conditional statement by solving the equation of our hypothesis. We will solve it by graphing. To do that, we will graph each side of the equation and find points of intersection.

The graphs intersect at both x=4 and x=-3. Therefore, the conditional statement is not true, as there is a second solution. Because it is not true, we cannot write a biconditional statement.