In a survey of 25 students, it was found that 12 have taken physics, 11 have taken chemistry and 15 have taken mathematics; 4 have taken physics and chemistry; 9 have taken physics and mathematics; 5 have taken chemistry and mathematics while 3 have taken all the three subjects. Find the number of students who have taken
(i) physics only; (ii) chemistry only; (iii) mathematics only; (iv) physics and chemistry but not mathematics; (v) physics and mathematics but not chemistry; (vi) only one of the subjects; (vii) at least one of the three subjects; (viii) none of the three subjects.