Sentence 1: The show is at its best on weekend afternoons, with everything from beach boys on unicycles to rock musicians on roller blades.

Sentence 2: Weekend afternoons are when the show is at its best.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: After quenching, the less corrosive flue gases entering the absorber decrease to temperatures of 49 - 66 eC with pH values between 5 and 6.5.

Sentence 2: Less corrosive flue gasses entering the absorber increased temperatures.
Is this second sentence entailed by the first?

Answer: no

Sentence 1: mail used by non-households to send and pay bills to other non-households).

Sentence 2: To send and pay bills to non-households, other non-households use mail.
Is this second sentence entailed by the first?

Answer:
yes