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 $x^{2} = 4$ ,then $x = - 2$ .

Short Answer

Expert verified

The statement “If $x^{2} = 4$ ,then $x = - 2$ .” is false, but the converse “If $x = - 2$ , then $x^{2} = 4$ ,” is true.

Step by step solution

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 “If p, then q” will be “If q, then p”.

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

If $x^{2} = 4$ ,then

$\begin{matrix} x = \sqrt{4} \\ = \pm 2 \end{matrix}$

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

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

The converse of the statement is: If $x = - 2$ then $x^{2} = 4$ ,

Here,

If $x = - 2$ , then

role="math" localid="1637650485182" $\begin{matrix} x^{2} = {(- 2)}^{2} \\ = 4 \end{matrix}$

Thus, the converse statement is true.

Therefore, the statement: " If $x^{2} = 4$ then $x = - 2$ " is false, but the converse of the statement: "If $x = - 2$ then $x^{2} = 4$ " is true.

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Tell whether each statement is true or false. Then write converse and tell whether it is true or false.
Statement: If $x^{2} = 4$ ,then $x = - 2$ .

Short Answer

Step by step solution

Step 1. Converse a conditional.

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

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

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Tell whether each statement is true or false. Then write converse and tell whether it is true or false.Statement: If x2=4,thenx=−2.

Short Answer

Step by step solution

Step 1. Converse a conditional.

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

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Logic and Functions

Applied Mathematics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.
Statement: If $x^{2} = 4$ ,then $x = - 2$ .