They are humans and strange monkeys on this island. You cannot tell who is who. They speak either only truths or only lies.

Who are the following to guys?

A:B is a lying monkey. I am human.

B:A is telling the truth.

If A is telling the truth, and B is lying. Meaning B's Statement is false, meaning that A is lying.

If B is telling the truth, that would mean that A is also telling the truth.

If A is Lying, then B is also lying.

Ergo they are either both lying, or both telling the truth.

If they are both Lying, then A is a monkey and B is human.

If they are both telling the truth, then B is the Monkey and A is Human. Therefore you can't tell who is who based on how you have written this problem.

If the rules were to state that only 1 can lie and only one can tell the truth, then we still can't tell, because Both statements are circular and both parties either have to be telling the truth or lying.

Just to clarify, it does hint at them both telling the truth, meaning A is human and b is the monkey. But A says that B is lying, and if that were true, then B's statement is false, as discussed, meaning that A is also Lying.