There live people and strange monkeys on this island, and you can not tell who is who. They speak either only the truth or only the lie. Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

Conjunction used by A is true only if both parts are true. Under the assumption that B is
an honest man, then A would be honest too (B says so) and so B would be a liar as A
said, which would be a conflict. So B is a liar. And knowing that, B actually said that A
is a liar, too. First statement of A is thus a lie and B is not a lying monkey. However, B
is lying which means he is not a monkey. B is a lying man. The second statement of A
indicates that A is a monkey – so A is a lying monkey.