Chapter 6: Q13. (page 205)

For the following conditional statement, classify the statement as true or false.
If $c > d$ and $e = f$ , then $c + e = d + f$ .

Short Answer

Expert verified

The conditional statement “If $c > d$ and $e = f$ then $c + e = d + f$ ” 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 $c > d$ and $e = f$ .

Adding e on both sides of the statement $c > d$ as follows:

$c > d c + e > d + e$

Step 3. Step description.

Now, the statement is $c + e > d + e$ .

Since $e = f$ substitute ffor ein the statement as follows:

role="math" localid="1637836987984" $c + e > d + e$

$c + e > d + f$

Thus, adding both sides to the same quantity doesn’t change inequality into equality.

Therefore, the statement is false.

Therefore, the conditional statement “if $c > d$ and $e = f$ then $c + e = d + f$ ” is false.

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For the following conditional statement, classify the statement as true or false.
If $c > d$ and $e = f$ , then $c + e = d + f$ .

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 c>dand e=f, then c+e=d+f.

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

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

For the following conditional statement, classify the statement as true or false.
If $c > d$ and $e = f$ , then $c + e = d + f$ .