There are 30 students in a class. 15 study woodwork and 13 study metal work.

Explanation

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,\(n(W ∩ M^1)\) = \(15 - x\)

Number of students that study only metalwork, \(n(W^1 ∩ M)\) = \(13 - x \)

Bringing all together,

\(n(W ∩ M^1)\) +\( n(W^1 ∩ M)\) + \(n(W ∩ M)\) + \(n(W ∪ M)^1\) = \(μ\)

∴ (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.