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In an university, out of 120 students, 1...

In an university, out of 120 students, 15 opted mathematics only, 16 opted statistics only, 9 opted for physics only and 45 opted physics and mathematics, 30 opted physics and statistics, 8 opted mathematics and statistics and 80 opted physics. By drawin Venn diagram, find the number of students who
(i) opted mathematics
(ii) opted statistics
(iii) did not opted any of the above three subjects.

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To solve the problem, we will use a Venn diagram to represent the relationships between the students who opted for Mathematics, Statistics, and Physics. We will denote the sets as follows: - Let \( M \) be the set of students who opted for Mathematics. - Let \( S \) be the set of students who opted for Statistics. - Let \( P \) be the set of students who opted for Physics. ### Given Data: - Total number of students = 120 ...
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