premise: A fire chief is determining the work schedules of five firefighters: Fuentes, Graber, Howell, Iman, and Jackson. The schedule must meet the following conditions: Except for Saturday and Sunday, when none of them works, exactly one of the firefighters works each day. None of the firefighters can work more than two days per week. No firefighter works on two consecutive days. Fuentes never works later in the week than Jackson. If Howell works, then Graber must work on the following day. If Graber does not work during the week, which one of the following statements must be true?
hypothesis: Iman works exactly two days during the week.