Chapter 2: Q23 (page 35)

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .

Short Answer

Expert verified

The statement " $a^{2} > 9$ if $a > 3$ ", " is true.

The converse of the given statement “If $a^{2} > 9$ then $a > 3$ .” is false.

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.

The statement " $a^{2} > 9$ if $a > 3$ ", Here the given statement is of the form q if p.

Here p is and q is $a^{2} > 9$ .

If $a > 3$ obviously $a^{2} > 9$ .

Therefore, the statement is true.

Step 3. Write the converse.

The converse is of the form "if q, then p“

Therefore, the converse of the given statement is – “If $a^{2} > 9$ then $a > 3$ .”

Step 4. State whether the converse is true or not.

In order to verify if the converse is true or not let $a^{2} = 16$ such that $a^{2} > 9$ .

But $a = \pm 4$ .

That is a maybe –4 which is less than 3.

Therefore, the converse of the given statement is false.

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Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .

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.

Step 4. State whether the converse is true or not.

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Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.a2>9if a>3.

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.

Step 4. State whether the converse is true or not.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Applied Mathematics

Statistics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$a^{2} > 9$ if $a > 3$ .