Chapter 6.1, Problem 6CE

To determine

To verify the conditional “If $a+b=n$ and $c>b$ , then $a+c>n$ .” is true or false.

Answer to Problem 6CE

True.

Explanation of Solution

Given:

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

Calculation:

Consider $c>b$

Adding $a$ on both sides, we get

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

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

Hence the given conditional is true.