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

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  1. 1
    3030 students were asked whether they play hockey (HH) and whether they play netball (NN).

    The Venn diagram shows the results.ξ3HN1278(a) Write down n(H∩N)n(H \cap N).

    (b) Find n(H∪N)n(H \cup N).

    (c) Write down n(H∩N′)n(H \cap N').
    Level 3 · 4 marksTry it
  2. 2
    ξ={1,2,3,…,15}\xi = \{1, 2, 3, \ldots, 15\}

    A={multiples of 3}A = \{\text{multiples of }3\}

    B={factors of 15}B = \{\text{factors of }15\}

    (a) List the members of A∩BA \cap B.

    (b) Find n(A∪B)n(A \cup B).

    (c) Ali says that n(A∪B)n(A \cup B) can always be worked out as n(A)+n(B)n(A) + n(B).

    Explain why Ali is wrong.
    Level 3 · 4 marksTry it