Question

Define a relation R on the set N of natural numbers by R = {( x , y ): y = x + 5, x is a natural number less than 4; x , y ∈ N }. Depict this relationship using roster form. Write down the domain and the range.

Answer 1

The given equation is,

y=x+5 (1)

Here, x is the natural number less than 4, i.e., 1, 2 and 3.

Substitute the value x=1 in the above equation (1).

y=1+5 y=6

Substitute the value x=2 in the above equation (1).

y=2+5 y=7

Substitute the value of x=3 in the above equation (1).

y=3+5 y=8

Therefore, the relation in roster form is,

R={ ( 1,6 ),( 2,7 ),( 3,8 ) }

The set of all first elements of the ordered pair in a relation R is called domain.

Domain of R={ 1,2,3, }

The set of all second elements of the ordered pair in a relation R is called range.

Range of R={ 6,7,8 }

Thus, the domain is { 1,2,3 } and the range is { 6,7,8 } .