one who answers I will do whatever they want
Solve the given worksheet:
In a survey of 25 students, it was found that 15 has taken Maths, 12 had taken Physics and 11 had
Chemistry, 5 has taken Maths and Chemistry, 9 had taken Maths and Physics, 4 had taken Physics and
and 3 had taken all the three. Find the number of students that had taken,
(1) Only Chemistry (ii) Only Maths (iii) Only Physics
(iv) Physics and Chemistry but not Maths (v) Maths and Physics but not Chemistry
(vi) Only one of the subjects (vii) At least one of the three subjects
(vii) None of the subjects
Pls answer
one with answer I will do whatever they want
Answers
Let M: Set of students who have taken Maths
P: Set of students who have taken Physics
C: Set of students who have taken Chemistry
Given,
Total students n(U) = 25
n(M) = 15, n(P) = 12, n(C) = 11
n(M ∩ C) = 5, n(P ∩ C) = 4, n(M ∩ P) = 9,
n(M ∩ P ∩ C) = 3
1. Number of students taking only Chemistry = n(C - (M ∪ P))
= n(C) - n(C ∩ (M ∪ P)
= n(C) - [n(C ∩ M) + n(C ∩ P) - n((C ∩ M) ∩ (C ∩ P)) ]
= n(C) - n(C ∩ M) - n(C ∩ P) + n(C ∩ M ∩ P)
= 11 - 5 -4 +3 = 14 - 9 = 5
2. Number of students taking only Maths = n(M - (P ∪ C))
= n(M) - n(M ∩ (P ∪ C))
= n(M) - [n(M ∩ P) + n(M ∩ C) - n((M ∩ P) ∩ (M ∩ C)) ]
= n(M) - n(M ∩ P) - n(M ∩ C) + n(M ∩ P ∩ C)
= 15 - 9 - 5 + 3
= 18 - 14
= 4
3. Number of students taking only Physics = n(P - (M ∪ C))
= n(P) - n(P ∩ (M ∪ C))
= n(P) - [n(P ∩ M) + n(P ∩ C) - n((P ∩ M) ∩ (P ∩ C)) ]
= n(P) - n(P ∩ M) - n(P ∩ C) + n(P ∩ M ∩ C)
= 12 - 9 - 4 + 3
= 15 - 13
= 2
4. Number of students taking Physics and Chemistry but not Maths = n((P ∩ C) - M)
= n(P ∩ C) - n(P ∩ M ∩ C)
= 4 - 3
= 1
5. Number of students taking Maths and Physics but not Chemistry = n((M ∩ P) - C)
= n(M ∩ P) - n(P ∩ M ∩ C)
= 9 - 3
= 6
6. Number of students taking only one subject = n((only M) + (only P) + (only C))
= n(only M) + n(only P) + n(only C)
= 4 + 2 + 5
= 11
7. Number of students taking at least one subject = n(M ∪ P ∪ C)
= n M) + n(P) + n(C) - n(M ∩ P) - n(P ∩ C) - n(M ∩ C) + n(M ∩ P ∩ C)
= 15 + 12 + 11 - 9 - 4 - 5 + 3
= 41 - 18
= 23
8. Number of students taking none of three subject = 25 - n(M ∪ P ∪ C)
= 25 - 23
= 2
hope it helps
Step-by-step explanation:
The answer will be 2.....