Chapter 1, Problem 4SGR

To determine

To state: whether given sentence is true or false and to make a true sentence.

Answer to Problem 4SGR

The statement is False, and the true sentence is “A solution of an equation is a value that makes the equation True”

Explanation of Solution

Given information:

Given statement,

“A solution of an equation is a value that makes the equation false”.

Calculation:

A solution of an equation is making the statement true, not false. By solving for example equation $x+1=0$ , we know that only solution for that is when $x=-1$ , which means that solution whatever it is making equation true.

  $\begin{array}{c}x+1=0\\ x=-1\end{array}$

Now, put the value $x$ in the example equation,

  $\begin{array}{c}-1+1=0\\ 0=0\end{array}$

Hence, the statement is False, and the true sentence is “A solution of an equation is a value that makes the equation True”