Three children recently born in a hospital were accidentally mixed up. The blood types of the parents involved are given below along with the blood types of the infants. Determine which baby belongs with which parents, and explain your reasoning for the decisions you made. Each child can only belong to one set of parents!
Parents #1: Mother Type A, Father Type B
Parents #2: Mother Type O, Father Type AB
Parents #3: Mother Type B, Father Type O
Child X: Type A
Child Y: Type O
Child Z: Type AB