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Chapter 6: Q13. (page 205)

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

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

Short Answer

Expert verified

The conditional statement 鈥淚f c>dand e=fthen c+e=d+f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 c>dand e=f.

Adding e on both sides of the statement c>das follows:

c>dc+e>d+e

03

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鈥檛 change inequality into equality.

Therefore, the statement is false.

Therefore, the conditional statement 鈥渋f c>dand e=fthen c+e=d+f鈥� is false.

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