The correct option is Only three pairs
Explanation
The Six Schools of Indian Philosophy, known as Shad Darshanas, are the orthodox (Astika) systems of thought. They are characterized by their acceptance of the authority of the Vedas as the supreme source of knowledge.
Statement-wise Analysis:
- Pair 1 is Correct: The Nyaya school, which focuses on logic and epistemology, was founded by Gautama (also known as Akshapada).
- Pair 2 is Correct: The Vaishesika school, known for its atomic theory and realistic pluralism, was founded by Kanada (also known as Uluka).
- Pair 3 is Incorrect: The Yoga school was founded by Patanjali. The sage Kapila is the founder of the Samkhya school, which is closely related to Yoga but distinct in its metaphysics.
- Pair 4 is Correct: The Vedanta school (specifically Uttara Mimamsa) is based on the philosophy of the Upanishads. Its foundational text, the Brahma Sutras, was composed by Badarayana, who is traditionally identified with Vyasa.
Key Takeaway:
The founders of the six orthodox schools are:
1. Nyaya: Gautama
2. Vaishesika: Kanada
3. Samkhya: Kapila
4. Yoga: Patanjali
5. Purva Mimamsa: Jaimini
6. Vedanta (Uttara Mimamsa): Badarayana (Vyasa)