Which of the following statements are correct as per Classical Indian School of logic (Nyaya)?

A. Nyaya syllogism has three propositions.
B. Nyaya syllogism has five propositions.
C. Nyaya syllogism has three terms.
D. Nyaya syllogism has five terms.
Choose the correct answer from the options given below:

The correct answer is B and C only.

According to the Classical Indian School of Logic (Nyaya), a syllogism (Anumana) has a specific structure consisting of propositions and terms that differs from Aristotelian syllogism. Let us analyze the statements step-by-step:

1. Number of Propositions (Statements A and B):
The Nyaya syllogism consists of exactly five propositions (known as Avayavas or members). These five members are:
1. Pratijna (Proposition/Promise): The statement to be proved (e.g., "The hill has fire").
2. Hetu (Reason): The ground or reason for the assertion (e.g., "Because it has smoke").
3. Udaharana (Example): The universal proposition showing the connection between the reason and the asserted fact, supported by a concrete example (e.g., "Wherever there is smoke, there is fire, as in a hearth").
4. Upanaya (Application): The application of the universal proposition to the present case (e.g., "This hill has smoke which is invariably associated with fire").
5. Nigamana (Conclusion): The conclusion drawn from the preceding propositions (e.g., "Therefore, this hill has fire").
Therefore, statement B is correct and statement A is incorrect.

2. Number of Terms (Statements C and D):
Like Western syllogistic logic, the Nyaya syllogism involves exactly three terms:
1. Sadhya (Major Term): The object or property to be inferred/proved (e.g., "fire").
2. Paksha (Minor Term): The subject or locus where the property is inferred (e.g., "hill").
3. Hetu or Linga or Sadhana (Middle Term): The reason or sign that indicates the presence of the major term in the minor term (e.g., "smoke").
Therefore, statement C is correct and statement D is incorrect.

Combining the correct statements, we get B and C only.