To answer this question, let's analyze the statements made by the two children:
Child A: "I am a boy" - said the child A with black hair.
Child B: "I am a girl" - said the child B with white hair.
If both statements were true, then Child A would indeed be a boy and Child B would be a girl. However, we are told that at least one of them lied.
If Child A is telling the truth, then Child B must be lying because they cannot both be telling the truth. But if Child B is lying about being a girl, then Child A must also be lying about being a boy because they both cannot be telling the truth.
Therefore, the correct answer is B) Both. Both Child A and Child B are lying.