Explanation:

The Atom Theory: The Vaisheshika School, founded by sage Kanada, is known for its atomic theory. According to this school, all physical substances are reducible to a number of ultimate indivisible particles or atoms (paramanu). So, it's the Vaisheshika School, not the Nyaya School, that propounded the Atom Theory. Hence, the statement "The Atom Theory was propounded by the Nyaya School of Philosophy" is incorrect.

Vaisheshika School and Logic: While the Vaisheshika School dealt with categories or "padarthas" and is often associated with metaphysical and cosmological explanations (including the aforementioned atom theory), it's the Nyaya School, founded by sage Gautama, that is known for its systematization of logic and epistemology. Nyaya's primary focus is on knowledge and its means. Thus, the statement "The Vaisheshika School was developed as a system of logic" is incorrect.