19N.1.SL.TZ0.T_4

pestleMathematicsAISLPaper 119N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Let the universal set, $U$ , be the set of all integers $x$ such that $1$ ≤ $x$ < $11$ .
$A$ , $B$ and $C$ are subsets of $U$ .

$A = \left\{ {1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}8} \right\}$
$B = \left\{ {2{\text{, }}3{\text{, }}5{\text{, }}7} \right\}$
$C = \left\{ {1{\text{, }}2{\text{, }}3{\text{, }}5{\text{, }}7{\text{, }}9} \right\}$

Write down $n\left( B \right)$ .

[1]

Complete the following Venn diagram using all elements of $U$ .

[4]

Write down an element that belongs to ${\left( {A \cup B} \right)^\prime } \cap C$ .

[1]

Markscheme / solution

$4$ (A1) (C1)

[1 mark]

(A1)(A1)(A1)(A1) (C4)

Note: Award (A1) for $3$ in the correct place. Award (A1) for $1$ , $2$ , $5$ and $7$ in the correct places. Award (A1) for $4$ , $6$ , $8$ , $9$ in the correct places. Award (A1) for $10$ outside of the three circles and $11$ not shown in the diagram.

If any entry is duplicated within its region, award at most (A3).

[4 marks]

9 (A1)(ft) (C1)

Note: Award (A1) for the correct element. Follow through from their Venn diagram in part (b). Award (A0) if additional incorrect elements are included in their answer.

[1 mark]

Examiners’ report

[N/A]