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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>4then5b>20

Short Answer

Expert verified

The statement 鈥淚f b>4then 5b>20.鈥� is true and the converse 鈥淚f 5b>20then b>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.

Since b>4,let b=5,then

5b=55=25

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

03

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

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

Here,

5b>20b>205b>4

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

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

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Most popular questions from this chapter

Justify each statement with a property from algebra or property of congruence.

If AB=CD,CD=EFand EF=23then AB=23.

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