By giving a counterexample,show that the following statement is not true.
$q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.

(N/A) The given statement is: $q:$ The equation $x^{2}-1=0$ does not have a root lying between $0$ and $2$.
To prove this statement false,we need a counterexample.
Consider the equation $x^{2}-1=0$.
Solving for $x$:
$x^{2} = 1$
$x = \pm 1$
The roots of the equation are $x = 1$ and $x = -1$.
Since the root $x = 1$ lies between $0$ and $2$,the statement that there is no root between $0$ and $2$ is false.