Page 11 - Mathematics_Form_3

Relations

Many-to-one relations
R A many-to-one relation is a relation in
A B which at least two elements from the
1 2 first set are mapped onto one element of
2 4 the second set. For instance, a relation
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3 6 ʻ a child of̕ defined as R = {(Haruna,
4 8 Khasim), (Khalid, Khasim), (Maimuna,
5 10 Khasim), (Anes, Joseph), ( Juliet,
Joseph)} is a many-to-one relation
Figure 1.4: Pictorial diagram of a because Haruna, Khalid, and Maimuna
one-to-one relation are children of Khasim, while Anes
and Juliet are children of Joseph.
Example 1.2 The respective mapping diagram of
a relation R, ‘is a child of’ is shown in
Let R = {(a, b ): b = 2a, where a ∈ A Figure 1.5.
and b ∈ B} . If A = {1, 2, 3} , draw a
pictorial representation to illustrate the ʻchild of̕

relation R.
Haruna
Solution Khasim
Khalid
From the relation, b = 2a. Maimuna

If a = 1, then b = 2; Anes
Juliet Joseph
If a = 2, then b = 4; Figure 1.5: Pictorial diagram of a
Mathematics for Secondary Schools R is shown in the following figure. One-to-many relations
If a = 3, then b = 6 .
many-to-one relation
A pictorial representation of the relation

A one-to-many relation is a relation
b=2a
in which one element of the first set is
B
A
mapped onto more than one element of
2
the second set. For instance, the relation
1
2
(4, 2) , (4, − 2) , (9, 3) } is a one-to-many
relation. The pictorial representation of
6
3 4 R = { (0, 0) , (0, – 3 ), (1, − 1) , (1, 1) ,
the relation R is shown in Figure 1.6.

4 Student\s Book Form Three

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