Page 26 - Mathematics_Form_3

Relations

Given a relation R, one can form another Remarks: It is observed from Example

relation from R by reversing the order in 1.19 that, the domain of R is the
−1
the ordered pairs belonging to R. This range of R and the range of R is the
−1
new relation is called the inverse relation domain of R. These statements are
FOR ONLINE READING ONLY
−1
of R and is denoted by R . The symbol generally true for any relation.
R is read ʻR inverse̕ or ʻ the inverse
−1
of R. ̕ Pictorial representation of the inverse
Let R be a relation where the elements of a relation
of set A are mapped onto members of The pictorial representation of inverse
set B. Then, R is the relation mapping of a relation R is obtained by reversing
−1
the elements of set B onto elements the direction of all arrows in R.
of set A. This relation is defined by

R = {(b, a ) : (a, b ) belongs to R} . Example 1.20
−1
Given the relation R as follows. Draw
Example 1.19
−1
the pictorial representation of R
Let R be the relation given by
R = {(a, b ) , (c, d ) , (e, f ) , (t, s)} . R

Find the: a p
(a) Domain of R. q

(b) Range of R. b r
(c) Inverse of R. s
c
(d) Domain of R .
−1
Domain of R Range of R
(e) Range of R .
−1
Solution
Solution
The pictorial representation of R is as
−1
(a) The domain of R is {a, c, e, t}.
shown in the following figure
(b) The range of R is {b, d, f, s}. Mathematics for Secondary Schools
(c) To find R , interchange positions

−1
of the x and y values in each pair. p a
Hence, q b
R = {(b, a ), (d, c ), (f, e ), (s, t)} . r
−1
s c
(d) The domain of R is {b, d, f, s } .
−1
(e) The range of R is {a, c, e, t } . Domain of R -1 Range of R -1
−1

Student\s Book Form Three 19

18/09/2025 09:58:43
MATHEMATIC F3 SB.indd 19 18/09/2025 09:58:43
MATHEMATIC F3 SB.indd 19