Sentence 1: There were a number of claimants to the throne, among them John Balliol, Lord of Galloway, and Robert de Brus, Lord of Annandale.

Sentence 2: Several people applied to sit at the throne.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: As you know, the Roman and the Ottoman empires suffered from grave internal weaknesses but persisted for centuries.

Sentence 2: Despite serious internal weaknesses, the Roman empire persisted for centuries.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: No, sir! We were attacked, the story would not match up if checked but it was close enough and Ca'daan was desperate.

Sentence 2: Ca'daan was desperate to believe what he was being told.
Is this second sentence entailed by the first?

Answer:
yes