Question

Out of 30 students in college 15 takes art courses, 8 takes biology courses and 6 takes chemistry. It is also known that 3 students take all the three courses. Show that 7 or more students taken none of the course

Answer 1

There are total 30 students.
Out of which 3 took all the three courses. So, students remained = 30 - 27.
Students who took arts course = 15, out of these 15 students, 3 students are also included who took all the three courses.
Students who took biology course = 8, out of these 8 students, 3 students are also included who took all the three courses.
Students who took chemistry course = 6, out of these 6 students, 3 students are also included who took all the three courses. 
So, number of students who took courses.
= (15 - 3) = 12 (Arts)
    (8 - 3) =    5 (Biology)
    (6 - 3) =    3 (Chemistry)
                    3  (Took all the three students)
_____________________
Total =        23 Students
_____________________

30 - 23 = 7 
So, the number of students who took none of the courses = 30 - 23 = 7
Answer.

A  Venn Diagram is attached with this question.

Answer 2

Answer:

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