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Chapter 2: Q18 (page 35)

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

Statement: If x2=4,thenx=鈭�2.

Short Answer

Expert verified

The statement 鈥淚f x2=4,then x=鈭�2.鈥� is false, but the converse 鈥淚f x=鈭�2, then x2=4,鈥� is true.

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.

If x2=4,then

x=4=卤2

Thus, x may be +2as well. Hence, the statement is false.

03

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

The converse of the statement is: If x=鈭�2thenx2=4,

Here,

If x=鈭�2, then

role="math" localid="1637650485182" x2=鈭�22=4

Thus, the converse statement is true.

Therefore, the statement: " If x2=4then x=鈭�2" is false, but the converse of the statement: "If x=鈭�2then x2=4" is true.

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