Sets

The universal set is $\mathcal{E}=\{x:x\text{ is an integer},\ 40\le x\le50\}$, and $P=\{x:x\text{ is a prime number}\}$ while $Q=\{x:x\text{ is a multiple of }6\}$.

May/June 2015

The Venn diagram displays the sets $A$, $B$ and $C$.

May/June 2015

On the Venn diagram, shade the region that shows the subset $(P \cup Q)' \cap R$.

May/June 2016

The preferences of 50 students are surveyed to find out what kind of movie they enjoy watching.

May/June 2016

$\mathcal{E}=\{2,3,4,5,6,7,8,9,10,11,12\}$, while $A=\{x:x\text{ is prime}\}$, $B=\{x:x\text{ is even}\}$, and $C=\{x:x\text{ is a multiple of }5\}$.

May/June 2016

In a sports club $24$ members play basketball ($B$), $28$ play cricket ($C$), $16$ play football ($F$), $9$ play basketball and cricket, $11$ play cricket and football and $6$ play basketball and football. Five members take part in all three games, and eight members do none of these games.

May/June 2017

Describe the shaded region in the Venn diagram by using set notation.

May/June 2017

Use set notation to state which part of the Venn diagram is shaded.

May/June 2018

$\mathcal{E} = \{x : x \text{ is an integer } 1 \le x \le 18\}$, $A = \{x : x \text{ is a prime number}\}$, and $B = \{1, 2, 3, 4, 6, 9, 12, 18\}$.

May/June 2018

On the Venn diagram, shade the area represented by $B' \cap A$.

May/June 2019

Express the shaded part of the Venn diagram in set notation.

May/June 2019

Shade the region $A' \cap B \cap C$.

May/June 2021

Write, in set notation, the subset shown shaded in the Venn diagram.

May/June 2021

On the Venn diagram, shade the area represented by $P\cap Q'$.

May/June 2022

$\mathcal{E}=\{a,b,c,d,e,f,g,h,i,j\}$, $P=\{i,a,e\}$, $Q=\{j,i,h,g,f\}$, $R=\{g,f,e,d,c\}$.

May/June 2022

Shade the part of the Venn diagram that corresponds to $(A \cap B)' \cup (B \cap C)'$.

May/June 2023

Take $\mathcal{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$. Define $P = \{x : x \text{ is a multiple of } 3\}$, $Q = \{x : x \text{ is an odd number}\}$, and $R = \{x : x \text{ is a factor of } 24\}$.

May/June 2023

In the Venn diagram, shade the part that represents $P \cup Q$.

May/June 2024

On the Venn diagram, shade the area shown by $(A \cap B)'$.

May/June 2025

Take $\mathcal{E} = \{2,3,4,5,6,7,8,9,10,11,12\}$, $A = \{x : x \text{ is a prime number}\}$, and $B = \{x : x \text{ is a factor of } 36\}$.

May/June 2025

Shade the set $(A \cap B) \cup C$.

Oct/Nov 2015

Let $\mathcal{E} = \{84,85,86,87,88,89,90,91,92,93,94,95,96\}$, with $P = \{x : x \text{ is an even number}\}$ and $Q = \{x : x \text{ is a multiple of } 3\}$.

Oct/Nov 2016

On the Venn diagram, shade the part corresponding to the subset $(A \cap B)' \cup C$.

Oct/Nov 2016

Take $\mathcal{E}=\{x:x\text{ is an integer and }10\le x\le 20\}$, $A=\{x:x\text{ is an odd number}\}$, and $B=\{x:x\text{ is a multiple of }5\}$.

Oct/Nov 2017

$\mathcal{E} = \{0,1,2,3,4,5,6\}$, $P = \{x : x = 0,1,2\}$, and $Q = \{y : y = 0,2\}$.

Oct/Nov 2018

Out of a group of 35 people, 22 are wearing spectacles, 10 are wearing a hat, and 6 are wearing both spectacles and a hat.

Oct/Nov 2018

In this question, $\mathcal{E} = \{x : x \text{ is an integer } 1 \le x \le 10\}$, $A = \{x : x \text{ is a factor of } 20\}$, and $B = \{x : x \text{ is a multiple of } 4\}$.

Oct/Nov 2018

In the Venn diagram, shade the area that represents $C \cap (A \cup B)'$.

Oct/Nov 2019

The universal set is $\mathcal{E} = \{x : x \text{ is an integer } 1 \le x \le 16\}$ Let $A = \{x : x \text{ is an even number}\}$ Let $B = \{x : x \text{ is a square number}\}$ Let $C = \{x : x \text{ is a factor of } 100\}$

Oct/Nov 2019

Shade the subset $(P \cup Q) \cap R'$ on the Venn diagram.

Oct/Nov 2020

$P = \{1,2,3,4,5,6,7,8\}$, $Q = \{1,3,5,7,9,11\}$. Find $n(P \cup Q)$.

Oct/Nov 2020

Given $\mathcal{E} = \{1,2,3,4,5,6,7,8,9,10,11,12\}$, $X = \{2,3,5,7,11\}$ and $Y = \{1,2,3,4,5,6\}$.

Oct/Nov 2021

Forty students are available for three activities: Art $(A)$, Dancing $(D)$ and Gardening $(G)$. Five students do not join any of the activities. Twelve take Art only. Four take both Dancing and Gardening, but not Art. One student takes part in all three activities.

Oct/Nov 2021

Shade the part of the Venn diagram that represents $A \cap B$.

Oct/Nov 2022

Let the sets be defined as follows: $\mathcal{E} = \{x : x \text{ is an integer } 10 \leq x \leq 40\}$ $P = \{x : x \text{ is a multiple of } 6\}$ $Q = \{x : x \text{ is a square number}\}$

Oct/Nov 2022

In a sports club with $40$ members, $22$ are runners ($R$), $24$ are cyclists ($C$), $14$ sail ($S$), $3$ cycle and sail but do not run, $9$ run and cycle but do not sail, $5$ run and sail but do not cycle, and $6$ run only.

Oct/Nov 2023

A shop offers hats ($H$), scarves ($S$) and gloves ($G$). A set of $40$ people are asked which of these items they purchase in the shop. Part of the information is displayed in the Venn diagram.

Oct/Nov 2023

A theatre provides a singing lesson $(S)$, a dancing lesson $(D)$ and an acting lesson $(A)$. A group of $40$ people are surveyed about which lessons they attend.

Oct/Nov 2024

$\mathcal{E} = \{x \mid x \text{ is an integer}, 1 \le x \le 15\}$ $A = \{x \mid x \text{ is a multiple of } 3\}$ $B = \{x \mid x \text{ is a factor of } 30\}$

Oct/Nov 2024