If R is a binary relation on a set A define R–1 on A. Let R = {(a, b) : a, b ϵ W and 3a + 2b = 15} and 3a + 2b = 15}, where W is the set of whole numbers. Express R and R–1 as sets of ordered pairs. Show that
(i) dom (R) = range (R–1)
(ii) range (R) = dom (R–1)
If R is a binary relation on a set A define R–1 on A. Let R = {(a, b) : a, b ϵ W and 3a + 2b = 15} and 3a + 2b = 15}, where W is the set of whole numbers. Express R and R–1 as sets of ordered pairs. Show that
(i) dom (R) = range (R–1)
(ii) range (R) = dom (R–1)

Answer : 3a + 2b = 15

a=1 è b=6 a=3 è b=3 a=5 è b=0

R = {(1, 6), (3, 3), (5, 0)}

????−1 = {(6, 1), (3, 3), (0, 5)}

The domain of R is the set of first co-ordinates of R Dom(R) = {1, 3, 5}

The range of R is the set of second co-ordinates of R Range(R) = {6, 3, 0}

The domain of ????−1 is the set of first co-ordinates of ????−1

Dom(????−1) = {6, 3, 0}

The range of ????−1 is the set of second co-ordinates of ????−1

Range(????−1) = {1, 3, 5} Thus,

dom (R) = range (R–1) range (R) = dom (R–1)