Step 1: Rigveda and Sthapatyaveda.
Rigveda, the oldest Veda, focuses on creation, cosmology, and order. It is linked to Sthapatyaveda, which outlines architecture and construction, drawing from Rigvedic principles of cosmic order. Therefore, A aligns with I.
Step 2: Yajurveda and Gandharvaveda.
Yajurveda primarily concerns sacrificial rituals and mantras. It is associated with Gandharvaveda, which covers music, dance, and performance arts, often integral to sacrificial ceremonies. Thus, B corresponds to II.
Step 3: Samaveda and Dhanurveda.
Samaveda consists of chants and melodies used in rituals. It is connected to Dhanurveda, the science of warfare and archery, as rhythmic recitation was linked to discipline and martial training. Consequently, C matches with III.
Step 4: Atharvaveda and Ayurveda.
Atharvaveda contains hymns related to healing, medicine, and life. It is consequently linked with Ayurveda, the science of life and health. Hence, D aligns with IV.
Step 5: Conclusion.
The correct matching is A - I, B - II, C - III, D - IV.