There are 30 students in a class. 15 study woodwork and 1...
There are 30 students in a class. 15 study woodwork and 13 study metal work. 6 study neither of the 2 subjects. How many student study woodwork but not metal work?
13
11
5
9
Correct answer is B
Using the venn diagram above
μ = 30
n(W) = 15
n(M) = 13
n(W∪M)1=6
Let x = number of students that study both woodwork and metalwork
i.e. n(W ∩ M) = x
Number of students that study only woodwork,n(W∩M1) = 15−x
Number of students that study only metalwork, n(W1∩M) = 13−x
Bringing all together,
n(W∩M1) +n(W1∩M) + n(W∩M) + n(W∪M)1 = μ
∴ (15 - x) + (13 - x) + x + 6 = 30
⇒ 34 - x = 30
⇒ 34 - 30 = x
∴ x = 4
n(W ∩ M^1) = 15 - 4 = 11
∴ The number of students that study woodwork but not metalwork is 11.
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