Final answer:
Hazrat Hassan was older than Hazrat Imam Hussein. In Shia Islam, the legitimate caliphs had to be descendants of Ali, and the Shia were defined by their elevation of the family of Muhammad through his son-in-law Ali. The descendants of Salah al-Din ruled Egypt and Syria under the name Ayubids.
Step-by-step explanation:
The older of the two, between Hazrat Imam Hussein and Hazrat Hassan, is Hazrat Hassan. They were the grandsons of the Prophet Muhammad and sons of Ali and Fatimah. Hazrat Hassan was born in 625 CE, while Hazrat Imam Hussein was born in 626 CE. Therefore, the correct answer to the question is b) Hazrat Hassan.
It's important to note that in Shia Islam, the legitimate Caliphs had to be descended from a critical figure in Islamic history. This was not Abu Bakr, but rather Ali, who was both the cousin and son-in-law of Prophet Muhammad, born from his daughter Fatimah.
Furthermore, the earliest supporters of Ali, who eventually became the Shia, were distinguished by their elevation of the family of Muhammad through his son-in-law Ali, leading to the belief that leadership should remain within the Prophet's family.
As for the descendants of Salah al-Din, under what name did they rule Egypt and Syria is not directly related to the question at hand, but they ruled under the name of Ayubids, not the Almohads or Hohenstaufens.