Question

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

If $a+b=n$and $c>b$then $a+c>n$.

Short answer

The conditional statement “If $a+b=n$and$c>b$ then $a+c>n$” is true.

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 $c>b$.

Adding both sides of the statement as follows:

$\begin{array}{c}c>b\\ c+a>b+a\\ c+a>a+b\end{array}$

Step 3. Step description.

Simplify the statement as follows:

$\begin{array}{l}c+a>a+b\\ a+c>n\left[a+b=n\right]\end{array}$

Thus, if $a+b=n$and $c>b$then $a+c>n$.

Therefore, the conditional statement “if $a+b=n$and $c>b$then $a+c>n$” is true.