Question

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

If $c-5>45$, then $c>48$.

Short answer

The conditional statement “If $c-5>45$, then $c>48$” 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 $c-5>45$.

Adding 5 both sides of the statement as follows:

$\begin{array}{c}c-5>45\\ c-5+5>45+5\end{array}$

Step 3. Step description.

Simplify the statement as follows:

$\begin{array}{c}c-5+5>45+5\\ c>50\end{array}$

Thus, if $c-5>45$then $c>50$.

Therefore, the conditional statement “if $c-5>45$then $c>48$” is false.