## Set Theory

Some students appeared for a test having 4 sections: QA, LR, DI and VA. Every student clears the cut-off in one or more of these sections. 43, 42, 36 and 39 students cleared the cut-off of QA, LR, DI and VA respectively. Further it is known that:
I. 11, 12, 13 and 14 students cleared the cut-off in at least 2 more sections apart from DI, LR, VA and QA respectively.
II. The number of students who cleared the cut-off of QA and LR only is equal to those who cleared the cut-off of DI and VA only which is two more than those who cleared the cutoff of QA, LR and DI only.

III. The number of people who cleared the cut-off in QA and exactly one more section is equal to those who cleared cut-off in LR and exactly one more section but is 2 less than those who cleared cut-off in VA and exactly one more section.
IV. 15 students cleared the cut-off of QA only, 6 students cleared the cut-off of VA only, 4 students cleared the cut-off of LR and QA only whereas 6 students

1. How many students cleared the cut-off in more than 2 sections?

2. How many students cleared the cut-off in QA and LR but not in DI?

3. How many students cleared cut-off in all 4 sections?

4. What is the difference between the number of students who cleared cut-off in exactly one section and those who cleared cut-off in exactly 3 sections?