Question

Let R be a relation in N defined by R = { ( x, y ) / 2x + 3y = 30 ,where x, y∈ N}. Express R. Also find the domain and range.

Answer 1

Let R be a relation in N defined by R = { ( x, y ) / 2x + 3y = 30 ,where x, y∈ N}

To find : find the domain and range of R and also express R.

solution : we know the relation is the set of ordered pairs. domain of a relation is set of first elements of ordered pairs and range of a relation is the set of 2nd elements of ordered pairs.

now 2x + y = 30 , where x , y ∈ N

x = 1, y = 28 ; (1, 28)

x = 2, y = 26 ; (2, 26)

x = 3, y = 24 ; (3, 24)

x = 4, y = 22 ; (4, 22)

x = 5, y = 20 ; (5, 20)

x = 6, y = 18 ; (6, 18)

x = 7, y = 16 ; (7, 16)

x = 8, y = 14 ; (8, 14)

x = 9, y = 12 ; (9, 12)

x = 10, y = 10 ; (10, 10)

x = 11, y = 8 ; (11, 8)

x = 12, y = 6 ; (12,6)

x = 13, y = 4 ; (13, 4)

x = 14, y = 2 ; (14, 2)

Therefore the relation is R = {(1, 28), (2, 26), (3, 24), (4, 22), (5, 20), (6, 18), (7, 16), (8, 14), (9, 12), (10, 10), (11, 8), (12, 8), (12, 6), (13, 4), (14, 2)}

domain = {1, 2, 3, 4 ......, 13, 14}

range = {2, 4, 6, 8, ....... 26, 28}

Answer 2

The above give answer is the perfect duede