Page 14 - Mathematics_Form_3

Relations

Example 1.5
9. Let M = {(Actor 1, Movie X), (Actor 1, Movie Y), (Actor 1, Movie Z), (Actor 2, Movie X), (Actor 2, Movie Z) }.
M = {(Actor 1, Movie X), (Actor 1, Movie Y), (Actor 1, Movie Z), (Actor 2, Movie X), (Actor 2, Movie Z) }.
Use the values in the following table
M = {(Actor 1, Movie X), (Actor 1, Movie Y), (Actor 1, Movie Z), (Actor 2, Movie X), (Actor 2, Movie Z) }.
to represent the relation R that exists
between x and y in terms of the ordered
M = {(Actor 1, Movie X), (Actor 1, Movie Y), (Actor 1, Movie Z), (Actor 2, Movie X), (Actor 2, Movie Z) }.
FOR ONLINE READING ONLY
M = {(Actor 1, Movie X), (Actor 1, Movie Y), (Actor 1, Movie Z), (Actor 2, Movie X), (Actor 2, Movie Z) }. pairs, hence write its domain and range.
Draw an arrow diagram to show the −3 0.5 1 2 5 6
connection “is the actor of” from the − 6 1 2 4 10 12

relation in set M.
Solution
Domain and range of a relation From the given table a relation of
Suppose that R: A → B is a relation ordered pairs is:
between two sets A and B. It is read as, R = {( − 3, − 6 ) , (0.5, 1), (1, 2 ) ,
̔ relation R maps the elements of set A (2, 4 ) , (5, 10 ) , (6, 12)} .
onto set B ̕. The domain of this relation
is the set of all members of set A which The domain of R is a set of x values,
are related to a member of set B, that that is x = {− 3, 0 . 5, 1, 2, 5, 6} and
is, all members of set A which have the range of R is the set of y values, that
corresponding members in set B form is y = {− 6, 1, 2, 4, 10, 12} .
the domain of a relation R.
On the other hand, the range of a relation
is the set of all elements of set B which Example 1.6
are related to at least one element of set Given the following ordered pairs:
A, that is, all members of set B which {(1, 2 ) , (2, 1 ) , ( − 3, 4 ) , ( − 3, − 5 ) ,
have corresponding members in set A (2, 2 ) , ( − 8, 0 ) , ( − 8, − 3) };
form the range of a given relation. Range
can also be described as the set of values (a) Which ordered pairs belong to the
which correspond to a set of values of relation R = {(x, y ) : y > x} ?
the domain of the relation. In Figure 1.8, (b) State the domain and range of R.
the domain is A = {2, 3, 5} and the range
is B = {a, c, e, f, g} . Solution Mathematics for Secondary Schools
R (a) Choose all ordered pairs ( , ) in the
A B given set such that y > x.
2 a The ordered pairs which satisfy
c this condition are:
3 e { (1, 2 ) , ( −3, 4 ) , ( −8, 0 ) ,
f ( − 8, − 3 )}.
5 g
(b) Domain of R = {1, − 3, − 8} and
Figure 1.8: Illustration of domain and range of R = {2, 4, 0, − 3}.
range

Student\s Book Form Three 7

18/09/2025 09:58:36
MATHEMATIC F3 SB.indd 7 18/09/2025 09:58:36
MATHEMATIC F3 SB.indd 7