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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.

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