4MA0 Higher June 2016 Paper 4R Q18

EdexcelHigherOld spec4 marksSets

18 The Venn diagram shows a universal set \(\mathscr{E}\) and three sets \(X\), \(Y\) and \(Z\).

Venn diagram of sets X, Y and Z in a universal set: X only 7, X and Y only 4, Y only 3, all three 0, Y and Z only 3, outside 2, with the X and Z only and Z only regions empty

The numbers shown represent numbers of elements.

\(\mathrm{n}(X^{\prime}) = 14\)
\(\mathrm{n}(Z) = 14\)

(a) Complete the Venn diagram. (2)
(b) Find the value of
(i) \(\mathrm{n}(X \cup Z)\)
(ii) \(\mathrm{n}(X \cap Y^{\prime})\)
(2)
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