Sets 3

2 marks · Easy

Set A = {students who play guitar}, Set B = {students who play piano}, in a class of 28 students. Explain using set notation how you would find the number of students who play either guitar or piano, but not both.

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n((A \ B) ∪ (B \ A)) or n(A ∪ B) − n(A ∩ B)

Also accept: n(A ∪ B) − n(A ∩ B); n((A \ B) ∪ (B \ A)); n((A ∪ B) \ (A ∩ B))

Common mistakes: Giving just n(A ∪ B) or n(A) + n(B)

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Marking points

M1 · 1 mark · Correctly identifies that students who play either but not both are those in A or B minus those in both (the intersection).

A1 · 1 mark · Writes the set operation as n((A ∪ B) − (A ∩ B)), n((A \ B) ∪ (B \ A)), or equivalent.

Worked solution

The number of students who play either guitar or piano but not both is given by

Alternatively, it equals n(A ∪ B) minus n(A ∩ B):