Sets (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

In a class of 40 students:

• 28 wear glasses ($G$)

• 13 have driving lessons ($D$)

• 4 do not wear glasses and do not have driving lessons.

i) Complete the Venn diagram.  

[2]

ii) Use set notation to describe the region that contains a total of 32 students.  

[1]

$\mathcal{E}=\{0,1,2,3,4,5,6\}A=\{0,2,4,5,6\}B=\{1,2,5\}$

Complete each of the following statements.

$\begin{array}{l}A\cap B=\{..........................................\}\\ \\ \mathrm{n}\left(B\right)=................\\ \\ \{0,4,6\}=................\cap ................\\ \\ \{2,4\}................A\end{array}$

$M=\{x:x\mathrm{is}\mathrm{an}\mathrm{integer}\mathrm{and}2\le x<6\}$

i) Find $\mathrm{n}\left(M\right)$.  

[1]

ii) Write down a set $N$ where $N\subseteq M$ and $N\ne \varnothing$.

{.................................................. } [1]

40 children were asked if they have a computer or a phone or both. The Venn diagram shows the results.

Complete the Venn diagram.  

$C=\{x:x$ is an integer and $5<x<12\}$                 $D=\{5,10\}$

  Select the correct statement from the list below.  

$D=\varnothing C\cap D=\left\{10\right\}6\in DD\subseteq C$

Find  $\mathrm{n}(C\cup D)$.

Use set notation to complete the statements for the Venn diagram above.

i) $c$ .................... $X$  

[1]

ii) .................................. = $\left\{a,m,e\right\}$  

[1]

iii) $Y\cap Z$ = ..................................

[1]

The Venn diagram shows a universal set, $\mathcal{E}$ and sets $A,B$ and $C.$

12, 5, 9, 10, 6, 3, 4 and 8 represent the numbers of elements.

Find

i) $n(A\cup B)$

[1]

ii) $n(Aʹ\cap Bʹ)$

[1]

iii) $n\left(\right[A\cap B]\cup C)$

[1]

Shade the region $P\cup \left(Q\cap R\right)\text{'}$.

Shade the region  $(D\cap E)\text{'}\cap F$  in the Venn diagram below.

In each Venn diagram, shade the required region. 

In this Venn diagram, shade the region $(A\cup B\text{'})\cap C$.

The Venn diagram shows information about the number of elements in sets $A$, $B$ and $\mathcal{E}$.

$\mathrm{n}(A\cup B)=23$

Find the value of $x$.

$x=$................................................

$\mathrm{n}\left(\mathcal{E}\right)=20,\mathrm{n}=\left(P\right)10,\mathrm{n}\left(Q\right)=13$ and $\mathrm{n}(P\cup Q)\text{'}=5$.

Work out  $\mathrm{n}(P\cap Q)$.

You may use the Venn diagram to help you.

$\mathrm{n}(P\cap Q)=$................................................

List the elements of $\left(X\cup Y\cup Z\right)\text{'}$.

Find $\mathrm{n}\left(X\text{'}\cap Z\right)$.

In this Venn diagram, shade the region$M\text{'}\cup N\cup P$.

This Venn diagram shows information about the number of students who play basketball $\left(B\right)$, football $\left(F\right)$ and hockey $\left(H\right)$.

Find $\mathrm{n}\left(\left(B\cup F\right)\cap H\text{'}\right)$.

The Venn diagram below shows information about the number of gardeners who grow melons ($M$ ), potatoes ($P$ ) and carrots ($C$ ).

Find  $\text{n}\left(\right(M\cap P)\cup C\text{'}).$