IGCSE Math B 2.E Complementary sets Topic Practice

$\mathscr E$ is the universal set and A, B and C are three sets where
$$\mathscr E=\{\text{positive integers less than }13\},$$$$A=\{\text{multiples of }5\}, \quad B=\{\text{even numbers}\}, \quad C=\{\text{factors of }8\}.$$
The Venn diagram below can be used to show these sets.

List the elements of the set
$$(A\cup B\cup C)'.$$

$$\mathscr E=\{\text{even numbers between }1\text{ and }29\}$$$$A=\{\text{prime numbers}\}, \qquad B=\{\text{factors of }24\}.$$
List the elements of the set

B'

$\mathscr E=\{2,3,4,5,6,7,8,9,10\}$$P=\{\text{prime numbers}\}$$E=\{\text{even numbers}\}$$F=\{\text{factors of }36\}$

70 children were asked which flavours of ice cream they like from chocolate (C), vanilla (V) and strawberry (S).
5 children like chocolate and vanilla and strawberry.
15 like strawberry only.
12 like chocolate only.
8 like none of the flavours.
6 like strawberry and vanilla.
11 like chocolate and vanilla.
21 like strawberry.
35 like vanilla.

Write down all the elements of:

E'

$\mathscr E$ is the universal set and A and B are two other sets.
$$\mathscr E=\{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21\}$$$$A=\{7,8,9,10,11,12,13,14,15\}$$$$B=\{12,13,14,15,16,17,18,19,20\}$$
List the members of the set

$(A\cup B)'$.

A college has 220 students.
All students study at least one of Biology, Chemistry or Drama.

$\mathrm n(A)=58$, $\mathrm n(B\cap C\cap D)=x$, $\mathrm n(B\cap D)=48$, $\mathrm n(B\cap C\cap D')=35$, and $\mathrm n((B\cup C)'\cap D)=20$.

The incomplete Venn diagram shows some of this information.

Given that $\mathrm n(C')=105$, find the value of x.

A youth club has introduced three new activities:

badminton (B), cookery (C) and drama (D).

Each of the 75 members of the youth club is asked to say in which of these activities they have participated.

Their answers showed that of the 75 members:

all have participated in at least one of these activities;
27 have participated in badminton and drama;
31 have participated in badminton and cookery;
23 have participated in cookery and drama;
48 have participated in badminton;
49 have participated in cookery;
40 have participated in drama.

Let x be the number of members of the youth club who have participated in all three activities.

Find

$n\left([(B\cap C)\cup D]^\prime\right)$

$15 \mathscr{E}=\{1,2,3,4,5,6,7,8,9\}$$A=\{2,4,6,8\}$$B=\{1,3,5,7,9\}$$C=\{2,3,5,7\}$

List the elements of the set

$(A \cap B)^{\prime}$
(3)

$16 \mathscr{E}=\{$ integers $x: 1 \leqslant x \leqslant 14\}$

In a survey of 55 farmers who keep animals, the numbers of farmers who keep cattle (C), goats (G) and sheep (S) were recorded.
The Venn diagram shows information about the results of the survey.
The numbers shown in the Venn diagram are the number of farmers in the given subset of $\mathscr E$.

Describe the members of the subset $C'\cap G'\cap S$.

$24 \mathscr{E}$ is the universal set and A, B and C are three sets where
$\mathscr{E}=\{$ positive integers less than 15$\}$$A=\{$ odd numbers $\}$$B=\{$ factors of 12 $\}$$C=\{$ multiples of 3$\}$

Find $\mathrm{n}\left([A \cup B \cup C]^{\prime}\right)$