Step 1: The stream is opened with the append mode flag:
ofstream file("example.txt", ios::app);
Step 2: The ios::app flag means every write goes to the end of the file. It does not erase the existing contents. This is different from the default ofstream open, which truncates the file to empty.
Step 3: If example.txt does not exist yet, opening it in append mode still creates a fresh empty file, then writes at the end.
Step 4: So the program writes the text \( Hello \) at the end of the file when it exists, and creates the file first when it does not. Then it closes the stream cleanly.
Answer: option A.