Statement (A):
While Australia is globally known for its enthusiasm for outdoor sports, it is not necessarily referred to as a "proud legacy" in the historical or cultural sense the way yoga is for India or martial arts for East Asia. So this statement is not technically considered part of a legacy.
Statement (B):
True. Yoga originated in ancient India and is deeply rooted in Indian spiritual and physical discipline. It is globally recognized today but remains a proud cultural and spiritual legacy of India.
Statement (C):
False. Martial arts are primarily associated with East Asian countries such as China, Japan, and Korea — not Germany. Germany is not historically known for developing or nurturing martial arts as a legacy.
Statement (D):
True. Gymnastics has historical roots in ancient civilizations, particularly in Greece and Rome, where physical training and development of the body were highly valued, especially for military readiness and cultural development.
Step 4: Final Answer
Hence, the correct statements are (B) and (D) only.