GCSE · Venn diagrams & set notation

Set notationExam-style questions

The formal language of sets — the universal set ξ, n(A) for a count, union A∪B ("in either, or both"), intersection A∩B, the complement A′, and combined expressions such as A∩B′ and (A∪B)′ — read as names for regions of a Venn diagram.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$\xi$ is the set of the $60$ students in Year 11 at a school.

$A$ is the set of students who have a part-time job.

$B$ is the set of students who play a musical instrument.

$n(A) = 34$ , $n(B) = 29$ and $n(A' \cap B') = 8$ .

(a) Find $n(A \cup B)$ .

(b) Find $n(A \cap B)$ .

(c) Find $n(A \cap B')$ .
Level 5 · 5 marksTry it
2
$\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$

$A = \{\text{multiples of }4\}$

$B = \{\text{even numbers}\}$

$C = \{\text{multiples of }5\}$

(a) Explain why $A \subset B$ .

(b) Write down $n(A \cap C)$ .

(c) List the members of $(B \cup C)'$ .
Level 5 · 5 marksTry it