Step 1: Understanding the Concept:
Horton-Strahler stream ordering defines the hierarchical topology of river drainage networks based on tributary confluence rules.
Key Formula or Approach:
\[ \text{Order}(u + u) = u + 1, \quad \text{Order}(u + v) = \max(u, v) \quad (u \neq v) \]
Step 2: Detailed Explanation:
Under Strahler's stream ordering system:
- Fingertip unbranched tributaries are First-order streams.
- When two first-order streams meet, they form a Second-order stream.
- When two second-order streams meet, they form a Third-order stream (Statement A).
- When lower-order streams join an existing higher-order stream, the order does not increase (e.g., joining an existing 3rd-order stream maintains 3rd-order status, Statement B).
- Joining two 3rd-order streams forms a 4th-order stream (Statement D).
Step 3: Final Answer:
Hence, the correct answer is A and B only, corresponding to option (A).