Sentence 1: (The New York City Department of Parks and Recreation has helpfully added a note that the work is not intended to promote cigarette smoking.

Sentence 2: New York parks and recreation added a note that ensured the work intended to promote cigarette smoking.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: kids with elderly people in the winter time they shovel their snow they have a big brother big sister program they have bottle drives they have cleanup outings

Sentence 2: The children go to places and help clean up, and also help those who can not shovel their snow in the winter.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: Napoleon named it Fort-de-France and that name was taken over for the town.

Sentence 2: Fort-de-France was named by Napoleon.
Is this second sentence entailed by the first?

Answer:
yes