Exercise
1A
1.
B is the set of odd positive integers less than 11.
4.
(a) List all the elements of D in set notation.
(a) List all the elements of B in set notation.
(b) Using the notation ∈ or ∉, describe whether
each of the following is an element of, or is
not an element of D.
(i) Tuesday
(ii) Sunday
(iii) March
(iv) Holiday
(b) State whether
whether each of the following statements
is true or false.
2.
(i) 1 ∈ B
(ii) 4 ∉ B
(iii) 0 ∈ B
(iv) 11 ∉ B
List all the elements in each
each of the following
following sets
in set notation.
D is the set of days in a week.
5.
P is the set of all perfect squares bigger than 1 and
less than 50.
(i) Is 10 ∈P?
(a) A = { x : x is a positive integer between 1 and
10}
(ii) List all the elements of P in set notation.
(b) B = {x : x is a negative integer between –10 and
6.
–1 inclusive}
(c) C = {x : x is a positive even integer such that
–2  x  12}
(a) I = {x : x is a colour of the rainbow}
(b) J = {x : x is a public holiday in Singapore}
(d) D is the set of vowels in the word ‘HAPPY’.
3.
(c) K is the set of consonants in the word
‘SYMMETRY.
List all the elements in each of the following sets in
set notation, and state whether it is an empty set.
(a) E is the set of odd numbers that are divisible
by 2.
List all
all the elements in each of the following
following sets
in set notation.
(d) L = {x : x is a teacher teaching my current
class}
7.
Describe each of the following sets in words.
(b) F = {x : x is a month of the year with more than
31 days}
(a) M = {0, 2, 4, 6, 8, …}
(c) G is the set of quadrilaterals with 5 vertices
each.
(c) O = {1, 8, 27, 64, 125, …}
(b) N = {0, 2, 4, 6, 8}
(d) P = {…, –15, –10, –5, 0, 5, 10, 15, …}
(d) H = {x : x is an even prime number}
8.
It is given that
Q = {x : x is a perfect square between 10 and 15}
and R = {x : x is a positive integer less than 5 that is
both a perfect square and a perfect cube}.
all the
the elements
elements of Q and of R in set
(i) List all
notation.
(ii) Are Q and R empty sets? Use the notation
Ø to describe Q and R.
007
Chapter 1
Sets
9.
State whether each of the following statements is
true or false. If it is false, explain why.
why.
11. State whether each of the following statements is
true or false. If it is false, explain why.
why.
(i) c ∉ {c, a, r}
(ii) car ∈ {c, a, r}
(i) {0} = Ø
(ii) Ø = { }
(iii) {c} ∈ {c, a, r}
(iv) {c, a, r} = 3
(iii) {Ø} is an empty set.
(iv) n(Ø) = 0
10. Describe the elements of each of the following sets
in set notation.
(a) S is the set of girls in my current class who
wear spectacles.
(b) T = {2, 3, 5, 7, 11, 13, …}
(c) U = {…, –8, –4, 0, 4, 8, 12, …}
(d) V = {–8, –4, 0, 4, 8, 12}
1.2
Venn Diagrams,
Universal Set and
Complement of a Set
We can represent a set using a Venn diagram as shown in Fig. 1.1.

A
4
1
AT
T
EN TI O N
2
3
5
Fig. 1.1
In Fig. 1.1, the rectangle represents the set of all the elements that are under
consideration for this particular situation, i.e. { 1, 2, 3, 4, 5}. This
This is called the universal
set and is denoted by the symbol ξ, i.e. ξ = {1, 2, 3, 4, 5}.
The circle represents the set A = {1, 2, 3}.
When drawing a Venn diagram,
• do not put commas between
the elements,
• do not write the elements too
close together,
• write the elements inside the
set, but label the set ξ or the
set A outside the set (i.e.
outside the rectangle or the
circle respectively).
We observe that the elements 4 and 5 are outside the circle but inside the rectangle,
i.e. 4 ∉ A and 5 ∉ A. The set of all the elements in ξ but not in A is called the
complement of the set A, and is denoted by A (pronounced as ‘A prime’),
i.e. A = {4, 5}.
Sets
Chapter 1
008