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Chapter 6: Q16. (page 205)

For the following conditional statement, classify the statement as true or false.

If a>b, then 100-a>100-b.

Short Answer

Expert verified

The conditional statement 鈥淚f a>bthen 100-a>100-b鈥� is false.

Step by step solution

01

Step 1. Apply the concept of a conditional statement.

Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also called the 鈥淚f-then" statement.

02

Step 2. Simplify the statement.

Consider the statement a>b.

Take negative sign both sides to the equality a>bas follows:

a>b

-a>-b

Now, the negative sign both sides to the inequality then the sign of inequality change.

-a<-b

03

Step 3. Step description.

Now, the statement is -a<-b.

Add 100 on both sides of the equation obtained.

-a+100<-b+100

100-a<b-100

Hence, the statement is false.

Therefore, the conditional statement 鈥渋f a>bthen 100-a>b-100鈥� is false.

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