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 “If $a > b$ then $100 - a > 100 - b$ ” is false.

Step by step solution

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 “If-then" statement.

Step 2. Simplify the statement.

Consider the statement $a > b$ .

Take negative sign both sides to the equality $a > b$ as follows:

$a > b$

$- a > - b$

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

$- a < - b$

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 “if $a > b$ then $100 - a > b - 100$ ” is false.

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For the following conditional statement, classify the statement as true or false.
If $a > b$ , then $100 - a > 100 - b$ .

Short Answer

Step by step solution

Step 1. Apply the concept of a conditional statement.

Step 2. Simplify the statement.

Step 3. Step description.

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For the following conditional statement, classify the statement as true or false.If a>b, then 100-a>100-b.

Short Answer

Step by step solution

Step 1. Apply the concept of a conditional statement.

Step 2. Simplify the statement.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Geometry

Decision Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

For the following conditional statement, classify the statement as true or false.
If $a > b$ , then $100 - a > 100 - b$ .