Exponential and Logarithmic Functions

Consider the following statements
\(\mathrm{A}\): \(\quad \log_{10}{(10^x)} > 0\)
\(\mathrm{B}\): \(\quad -0.5 \leq \cos{(0.5x)} \leq 0.5\)
\(\mathrm{C}\): \(\quad -\frac{\pi}{2} \leq \tan^{-1}{x} \leq \frac{\pi}{2}\)[6]

1. Determine which statements are true for all real numbers \(x\). Write your answers (yes or no) in the table below.

   Statements	(a) Is the statement true for all real numbers \(x\)? (Yes/No)	(b) If not true, example
   \(\mathrm{A}\)
   \(\mathrm{B}\)
   \(\mathrm{C}\)

2. If a statement is not true for all \(x\), complete the last column by giving an example of one value of \(x\) for which the statement is false.