In which of the five steps of inference (anuma̅na) in the Nya̅ya syllogism all the three terms stand synthesized? 

Nyaya, (Sanskrit: “Rule” or “Method”) is one of the six systems (darshans) of Indian philosophy, important for its analysis of logic and epistemology. The major contribution of the Nyaya system is its working out in profound detail the means of knowledge known as inference.

Important Points

• Anumana is a Sanskrit word that means “inference” or “knowledge that follows.” It is one of the pramanas, or sources of correct knowledge, in Indian philosophy.
• Anumana is using observation, previous truths, and reason to reach a new conclusion and truth.
• Anumana consists of five steps: a hypothesis (pratijna), reason (hetu), an example (udaharana), reaffirmation (upanayana), and conclusion (nigamana).
• Paksa – The Thesis / Pratijna Proposition, The hill has fire
• Hetu – Reason or the ground, Because it has smoke.
• Drstanta – The corroboration, wherever there is smoke there is fire, as in the kitchen.
• Upanaya – The application, the hill is so.
  Nigamana – the conclusion. Therefore the hill has fire.

​Therefore with the given information, we can conclude that Upanaya of Nyaya Philosophy has all the terms synthesized.