Step 1: Understanding the Concept:
Amino acids are classified by two main criteria:
1. Nutritional Requirement: "Essential" amino acids cannot be made by the body and must come from food. "Non-essential" ones can be synthesized internally.
2. Side-chain Chemistry: "Basic" amino acids have extra amine ($-NH_2$) groups in their side chains. "Neutral" amino acids have an equal number of amine and carboxyl groups.
Step 2: Detailed Explanation:
Let's analyze the given list:
- Lysine (a): Essential and Basic (contains an extra $-NH_2$ group). Fits Category X.
- Arginine (d): Semi-essential (usually classed as essential for exams) and Basic (contains a guanidino group). Fits Category X.
- Alanine (b): Non-essential and Neutral (alkyl side chain). Fits Category Y.
- Serine (c): Non-essential and Neutral (polar side chain). Fits Category Y.
- Tyrosine (e): Non-essential and Neutral (aromatic side chain). Fits Category Y.
Thus, $X = \{a, d\}$ and $Y = \{b, c, e\}$.
Step 3: Final Answer:
This maps to option (B).