2.1 The Domain of a Relation
Consider a relation R that maps elements from set A to set B. The domain of relation R is defined as
the set of all elements an in set A, such that there exists an element b in set R for which the ordered
pair (a,b) belongs to relation R. The domain of the function R can be precisely denoted as “domain
R.” The domain of the relation R is defined as the set of elements an in set A such that there exists
an element b in set B for which the pair (a, b) is an element of R. The domain of a relation R is
defined as the set of first components of all the ordered pairs that belong to R.

2.2 The Domain and Codomain of a Relation
Consider a relation R that maps elements from set A to set B. The range of the relation R is defined
as the set of all elements b in the set R, such that there exists an element an in the set A such that
(a,b) is an element of R. The range of a relation R is defined as the set of elements b in the set B,
such that there exists an element an in the set A for which the pair (a,b) is in the relation R. The
range of a relation R is defined as the set of second components of all ordered pairs that belong to
R. The set B is referred to as the codomain of the relation R.

Consider the sets A and B, where A is defined as {2, 3, 5} and B is defined as {4, 7, 10, 8}.Let the
statement aRB be equivalent to the statement “a divides b.”Let R be a relation defined as R = {(2,5)}.
The range of R, denoted as range(R), is given by range(R) = {4,10,8}.The codomain of the relation R =
B = {4,7,10,8} is the set {4,7,10,8}.

Consider the sets A = {1,2,3} and B = {2,4,6,8}.Let R be a relation defined from set A to set B, where
xRy is true if and only if The value of y is twice that of x, for all x belonging to set A.The relationships
between the numbers are as follows: 1R2, 2R4, and 3R6.Hence, the relation R can be represented as
follows: R = {(1,2), (2,4), (3,6)}.