Question

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

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:

$$\begin{gathered} c>d \\ c+e>d+e \end{gathered}$$

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.