The true statement is now presented: If [tex]c > 0[/tex] and [tex]|u| > c[/tex], then [tex]u > c[/tex] or [tex]u < -c[/tex].
Mathematically speaking, the absolute value is defined by following expression:
[tex]|a| = \left \{ {{a,\,a \ge 0} \atop {-a,\,a < 0}} \right.[/tex] (1)
If [tex]c > 0[/tex] and [tex]|u| > c[/tex], then [tex]u > c[/tex] or [tex]-u > c[/tex]. Hence, [tex]u > c[/tex] or [tex]u < -c[/tex].
Therefore, if [tex]c > 0[/tex] and [tex]|u| > c[/tex], then [tex]u > c[/tex] or [tex]u < -c[/tex]. (By tricotomy)
We kindly invite to see this question on absolute values: https://brainly.com/question/4691050
