Sets (Cambridge International IGCSE Maths): Exam Questions

Use set notation to describe the shaded region in each Venn diagram.

On the Venn diagram, shade the region $A\cap B$.

$E$ = {1, 2, 3, 4, 5, 6}

$P$= {$x$ : $x$ is an even number}

$Q$ = {$x$ : $x$ is a prime number}

Complete the Venn diagram.

Use set notation to describe the shaded regions in each Venn diagram.

i) $E$= {2, 4, 8, 16, 32, 64}

$A$ = {square numbers}

$B$ = {cube numbers}

Use this information to complete the Venn diagram.

ii) On this Venn diagram, shade the region $P\cup Q$.

In a group of 40 students,

• 24 students like football
• 19 students like cricket
• 10 students like football but not cricket.

Complete the Venn diagram.

$E$ = {children in a group} $R$= {children who own a rabbit} $H$ = {children who own a hamster}

There are 40 children in the group. 19 children own a rabbit. 27 children own a hamster.

Complete the Venn diagram.

Extract:

![R space]= {children who own a rabbit}

![H] = {children who own a hamster}

Write down $n ( R \cap H ) .$

The Venn diagram shows information about the number of students in a class who like apples ($A$) and bananas ($B$).

i) Work out the number of students in the class.

ii) Work out the number of students who like bananas.

iii) Work out $n ( A \cup B )$.

iv) How many more students like apples than like bananas?

$E$ = {$x$ : $x$ is a positive integer less than 20} A = {$x$ : $x$ is an even number} B = {$x$ : $x$ is a multiple of 3}

i) Write down $\mathrm{n} ( A )$.

ii) List the elements of set $B$.

$B$= { ............................................... } [2]

iii) Complete the statement.

$A \cap B = \{ x : x \text{is} ............................... \}$

$E$ = {$x$ : $x$ is a natural number less-than or slanted equal to15}

$F$ = {$x$ : $x$ is a factor of 12}

$O$ = {$x$ : $x$ is an odd number}

i) Complete the Venn diagram to show the elements of these sets.

ii) Write down one number that is in set $O$, but not in set $F$.

iii) Find $\mathrm{n} ( F \cup O )$.

$E$ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} $F$ = {$x$: $x$ is a factor of 14} $P$ = {$x$: $x$ is a prime number less than 14}

i) Write down the elements in set $F$.

$F$ = { ................................................ } [2]

ii) Write down the elements in set $P$.

$P$ = { ................................................ } [2]

iiia) Complete the Venn diagram.

iiib) Write down $n$($F\cap P$)

$E$= {children who go to the park} $T$= {children who play tennis} $G$ = {children who play golf}

120 children go to the park. 50 play tennis. 75 play golf. 25 do not play tennis or golf.

Complete the Venn diagram.

Extract:

![calligraphic E]= {children who go to the park}

![space T space]= {children who play tennis}

![G] = {children who play golf}

120 children go to the park.

50 play tennis.

75 play golf.

25 do not play tennis or golf.

Find n($T\cap G$).