Sentence 1: If you've installed Internet Explorer 4.0, click here for more about (and a chance to download) the channel.

Sentence 2: The channel will work if you have Internet Explorer 4.0 on your computer.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: She asked for a contact number for me, in case something happened in the building--like a water leak--so I feel that she has good intentions.

Sentence 2: She seems responsible because she asked for a way to report potential issues.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: When the last of the wealthy Rezzonico family disappeared, Elizabeth Barrett and Robert Browning bought the palazzo, and the poet died in a first-floor apartment in 1889.

Sentence 2: The wealthy Rezzonico family still live on today.
Is this second sentence entailed by the first?

Answer:
no