Statement I : Ashoka called the Third Buddhist Council in 252 BC at Pataliputra and it was there that the Buddhist Church became divided into two sects—the Hinayana and the Mahayana. Statement I : Kanishka called the Fourth Buddhist Council at Kundalvana near Srinagar and Vasumitra was believed to have acted as President.

Statement I is false because the Third Buddhist Council, held at Pataliputra under Ashoka's patronage around 250 BCE, focused on purifying the Sangha and establishing the Sthaviravada (Theravada) as the orthodox school. The formal division of Buddhism into the Hinayana and Mahayana sects did not occur during this council; rather, it is associated with the Fourth Buddhist Council. Statement II is true as the Fourth Buddhist Council was indeed convened by the Kushana king Kanishka at Kundalvana in Kashmir [2]. This council was presided over by Vasumitra, with Ashvaghosha as the vice-president [3]. It was during Kanishka's reign and this council that the Mahayana sect rose to prominence and the doctrinal split between Hinayana and Mahayana became distinct [2].

Sources

1. [1] History , class XI (Tamilnadu state board 2024 ed.) > Chapter 6: Polity and Society in Post-Mauryan Period > Kanishka > p. 80
2. [2] History , class XI (Tamilnadu state board 2024 ed.) > Chapter 3: Rise of Territorial Kingdoms and New Religious Sects > Decline of Buddhism in India > p. 43
3. [3] https://en.wikipedia.org/wiki/Buddhist_councils