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Chapter 2: Q17 (page 35)

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If x=鈭�6,thenx=6.

Short Answer

Expert verified

The statement is true, but the converse is false.

Step by step solution

01

Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement 鈥淚f p, then q鈥� will be 鈥淚f q, then p鈥�.

02

Step 2. State whether the statement is true or not.

It is known that x=鈭�xand x=鈭�6.

Thus,

x=鈭�鈭�6=6

Hence, the statement is true.

03

Step 3. Write the converse of the statement and verify.

The converse of the statement is: If x=6then x=鈭�6, but if x=6, it meansx=卤6.

Thus, the converse statement is false.

Therefore, the statement: "If x=鈭�6, then x=6" is true, but the converse of the statement: "If x=6, then x=鈭�6" is false.

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