Definition of Relation R:
The relation R is defined on the set A = {1, 2, 3, 4, 8} and is given by R = {(x, y) : x is a division of y}. In other words, R consists of ordered pairs (x, y) where x is a divisor of y.

Writing Relation R:
The relation R can be written as follows:
R = {(1, 1), (1, 2), (1, 4), (1, 8), (2, 2), (2, 4), (4, 4), (8, 8)}

Domain of Relation R:
The domain of a relation is the set of all first elements of the ordered pairs in the relation. In this case, the domain of relation R is the set of all x-values or divisors. Therefore, the domain of R is {1, 2, 4, 8}.

Range of Relation R:
The range of a relation is the set of all second elements of the ordered pairs in the relation. In this case, the range of relation R is the set of all y-values or dividends. Therefore, the range of R is {1, 2, 4, 8}.

Explanation:
The relation R is defined as the set of ordered pairs in which the first element (x) is a divisor of the second element (y). In other words, for any ordered pair (x, y) in R, x divides y without leaving a remainder.

For example, (1, 2) is in R because 1 is a divisor of 2. Similarly, (2, 4) is in R because 2 divides 4. On the other hand, (2, 3) is not in R because 2 does not divide 3 without leaving a remainder.

The set A = {1, 2, 3, 4, 8} represents the possible values for both x and y in the relation R. It includes all the potential divisors and dividends.

The relation R consists of eight ordered pairs: (1, 1), (1, 2), (1, 4), (1, 8), (2, 2), (2, 4), (4, 4), and (8, 8). These pairs represent the divisions that satisfy the condition of the relation.

The domain of R is the set of all x-values, which are the divisors in this case. Thus, the domain of R is {1, 2, 4, 8}.

Similarly, the range of R is the set of all y-values, which are the dividends. Therefore, the range of R is {1, 2, 4, 8}.

Overall, the relation R represents all possible divisions between the elements of set A, and its domain and range consist of the divisors and dividends involved in these divisions.