Edward, Howard, and John are three high school students each of whom is taking three of the four subjects, biology, chemistry, history, and mathematics. One day while talking about their programs they made the following statements.
Edward: There is just one subject we're all taking. I'm the only one of us who is taking mathematics. No two of us are taking the same three subjects. John is wrong when he says that Howard and I are both taking chemistry.
Howard: Ed is the only one of us who is taking history. John and I are taking the same subjects. We're all taking biology. Two of us are taking both chemistry and biology.
John: We're all taking mathematics. Howard is taking history. Ed is taking one subject that I'm not. Both Howard and Ed are taking chemistry.
If two and only two of each boy's statements are true, what subjects is each boy taking?