Sentence 1: However, if you want a room in a particular hotel, it is best to book, especially during July and August.

Sentence 2: Booking in July and August can be difficult because many people book during that time.
Is this second sentence entailed by the first?

Answer: it is not possible to tell

Sentence 1: The American Ambassador, Mr. Carter, who had taken the liberty, he said, of bringing an old friend, Sir William Beresford, with him, Archdeacon Cowley, Dr. Hall, those two youthful adventurers, Miss Prudence Cowley and Mr. Thomas Beresford, and last, but not least, as guest of honour, Miss Jane Finn.

Sentence 2: The American Ambassador, Mr. Carter, came alone, opting not to bring any guests.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: I am Jon, said the man, turning back to the polished metal.

Sentence 2: Jon was holding a metal gun.
Is this second sentence entailed by the first?

Answer:
it is not possible to tell