Chapter SH, Problem 10.25EP

To determine

To find: The counterexample to disprove the statement.

Answer to Problem 10.25EP

The statement disproves at $n=-1$ .

Explanation of Solution

Given: The statement is $n^2+4n-3$ is prime.

Consider the expression,

  $n^2+4n-3$

Substitute $-1$ for $n$ .

  $\begin{array}{c}{n}^2+4n-3={\left(-1\right)}^2+4\left(-1\right)-3\\ =1-4-3\\ =1-7\\ =-6\left(\text{Not}\text{prime}\right)\end{array}$

Therefore, the statement disproves at $n=-1$ .