Step 1: Understanding the reaction sequence.
- In the first step, the reaction of a carboxylic acid (P) with ammonia (\(\text{NH}_3\)) and heat leads to the formation of an amide (Q).
- In the second step, treatment of Q with \(\text{Br}_2\) in the presence of \(\text{KOH}\) (the Hofmann degradation reaction) removes one carbon from the amide, resulting in a primary amine (R).
Step 2: Analyzing the options.
(1) This option correctly represents the structures of P, Q, and R as per the reaction sequence. The first structure shows the carboxylic acid, the second shows the amide, and the third shows the amine.
(2) This option shows incorrect functional groups for Q and R.
(3) This option does not reflect the correct transformations in the reaction sequence.
(4) This structure is not consistent with the expected reaction products.
Step 3: Conclusion.
The correct answer is (1) as it correctly follows the reaction sequence from carboxylic acid to amide to amine.