4400 Higher November 2005 Paper 3 Q20

EdexcelHigherOld spec6 marksSets

20

Venn diagram: universal set E containing overlapping sets P and Q; x in P only, y in P and Q, 3 in Q only, w outside both

In the Venn diagram, 3, \(w\), \(x\) and \(y\) represent the numbers of elements.
\(\mathrm{n}(\mathscr{E}) = 24 \qquad \mathrm{n}(P') = 8 \qquad \mathrm{n}((P \cap Q)') = 15\)

(a) Find the value of
(i) \(w\)
(ii) \(x\)
(iii) \(y\) (3)
(b)
(i) Find \(\mathrm{n}(P' \cap Q)\).
(ii) Find \(\mathrm{n}(P' \cup Q')\).
(iii) Find \(\mathrm{n}(P \cap Q \cap P')\). (3)
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