Sentence 1: But still, I had many meetings with him, and he showed no signs of distraction or impatience.

Sentence 2: I met with him many times and noticed his behavior.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: He agreed that the authority issue is important, but he suggested smaller, targeted research studies could address that question.

Sentence 2: He said that the authority issue did not matter.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: It's a hobby that doesn't get too much time these days.

Sentence 2: Few people are interested in stamp collecting these days.
Is this second sentence entailed by the first?

Answer:
it is not possible to tell