This paper examined the ability of students to pose a problem in a free posing situation about sets in terms of the problem text, compatibility with mathematics principles, the problem type and structure, solvability, and mathematical complexity. Additionally, students were probed to determine the difficulties they encountered during the problem posing process. The descriptive qualitative research design made use of data collected through an open-ended assessment which is a free problem posing task, and an interview with students. Students' posed problems were evaluated using an adapted analytic rubric and interview transcripts were analyzed to determine student's problem posing skills and difficulties in the problem posing process, respectively. Results show that although students can generate problems, clarity of thoughts, problem difficulty, solvability and complexity level of the posed problems need to be further developed. Students' posed problems were textbook like and displayed low mathematical complexity level. Some students gave wrong solutions and/or answers among the solvable problems posed. Additionally, they had difficulties in writing clear and understandable text, concretizing the abstract direction of the problem posing process, providing given for the problem, adjusting the degree of difficulty and remembering the concepts learned. The findings suggest that problem posing is yet to be established as an important element in mathematics instruction.