Page 152 - Mathematics_Form_Two

Sets

Operations on sets Example 7�8
It is possible to combine two or more sets Find A∪B if A = {a, b, c, d, e, f} and
=
under specific conditions to obtain a new B {a, e, i, o, u}.
set. Engage in Activity 7.2 to experience Solution
set operations in real life. Given A {a, b, c, d, e, f} and
=
FOR ONLINE READING ONLY
B = {a, e, i, o, u}. It follows that,
Activity 7�2: Exploring set operations
Mathematics for Secondary Schools 1. Collect simple household items such Intersection of sets
}
{a, b, c, d, e, f, i, o, u
A ∪
B =

in daily life
Therefore, A∪B = {a, b, c, d, e, f, i, o, u}.
as lids of bottles, coloured buttons,
and fruits.
The intersection of sets, A and B is the set
2. Organise and compare sets of items
by combining them. Identify common
common to both sets. It is denoted by the
items and items which are not in the which contains all the elements that are
cap symbol “∩”. Thus,the intersection of
whole set, and then distinguish the sets A and B is written as A∩B, which
sets. means, x∈B∧B if x∈A and x∈B. The
3. Represent the sets in a method of your keyword for intersection is “and”.
choice and justify your categories. For example, if A = {1, 2, 3, 4, 5} and
B = {1, 3, 5}, then A∩B = {1, 3, 5}.

In Activity 7.2, one has performed Example 7�9
set operations in different ways by
categorizing and comparing, combining Find A∩B if A = {a, e, i, o, u} and
and identifying common items. B = {a, b, c, d, e, f} and state if A and
B are disjoint sets or not.
Set operations are categorized into Solution
four types namely: union, intersection, Given A = {a, e, i, o, u} and
complement, and set difference. These B = {a, b, c, d, e, f}, it follows
operations involve identifying elements that A∩B = {a, e}
in each set and determining the number of Therefore, A and B are joint sets.
elements involved.

Union of sets Example 7�10
The union of two or more sets is the set Find A∩B if A = {a, e, i} and
that contains all the elements of each set, B = {b, c, f}. State if A and B are
without any repetition. The union of sets is disjoint sets or not.
represented by the cup symbol ''∪''. Thus, Solution
A ∪ B denotes that an element x belongs

B
to A ∪ if and only if x∈ x A, x∈ or A, x∈ B ∈ B or Given A = {a, e, i} and B = {b, c, f}.
x is in both A and B. The keyword for the The sets A and B do not have common
union of sets is “or”. elements. Thus, A and B are disjoint
sets. Therefore, A ∩ B = ∅ .

146
Student's Book Form Two

11/10/2024 20:13:17
MATHEMATIC F2 v5.indd 146 11/10/2024 20:13:17
MATHEMATIC F2 v5.indd 146