Step 1: Where the trap lies.
Check the assertion and reason one at a time. The catch in this question is hidden in the single word 'increases' inside the reason, so read it carefully.
Step 2: Test the assertion.
The $\mathrm{-NH_2}$ group activates aniline so powerfully that plain bromination floods the ring and gives the tribromo product. By first converting $\mathrm{-NH_2}$ into $\mathrm{-NHCOCH_3}$ through acetylation, we calm the ring down and obtain a single bromo product. So the assertion is true.
Step 3: Test the reason.
Acetylation actually reduces the activating power of the amino group, because the nitrogen lone pair is now drawn towards the C=O group and is less available to the ring. The reason claims it increases the activation, which is the opposite of the truth, so the reason is false.
Step 4: Conclusion.
A true assertion paired with a false reason fits option (C).
\[ \boxed{\text{Option (C): A true, R false}} \]