Chapter 2: Q19 (page 35)

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.
Statement: If $b > 4$ then $5 b > 20$

Short Answer

Expert verified

The statement “If $b > 4$ then $5 b > 20$ .” is true and the converse “If $5 b > 20$ then $b > 4$ ,” 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.

Since $b > 4$ ,let $b = 5$ ,then

$\begin{matrix} 5 b = 5 (5) \\ = 25 \end{matrix}$

Thus, $5 b > 20$ .So, if $b = 5$ ,then $5 b > 20$ .Hence, the statement is true.

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

The converse of the statement is: If $5 b > 20$ then $b > 4$ ,

Here,

$\begin{matrix} 5 b > 20 \\ b > \frac{20}{5} \\ b > 4 \end{matrix}$

So, if $5 b > 20$ then $b > 4$ . Thus, the converse statement is true.

Therefore, the statement: " If $b > 4$ ,then $5 b > 20$ ." is true, but the converse of the statement: " If $5 b > 20$ .then $b > 4$ ," 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 $b > 4$ then $5 b > 20$

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 b>4then5b>20

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

Pure Maths

Mechanics Maths

Applied Mathematics

Logic and Functions

Statistics

Theoretical and Mathematical Physics

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 $b > 4$ then $5 b > 20$