There are five questions below，

Seven science students—John, Kate, Luz, Mark, Nelson, Olga, and Pat—are to be divided into three groups. One group will consist of three students, and the other groups will consist of two students each. The following conditions apply to the assignment of students to groups:

John cannot be assigned to the group to which Luz is assigned.

Nelson must be assigned to the group to which Pat is assigned.

Olga must be assigned to the group consisting of three students.

Which of the following is an acceptable assignment of students to groups?

If one of the groups of two consists of Luz and Mark, which of the following must be true?

If Nelson is assigned to the group to which Olga is assigned, which of the following can be true?

If Mark is assigned to a group to which neither John not Pat is assigned, which of the following must be true?

If John and Olga are assigned to different groups from each other, which of the following CANNOT be true?