Consider the set A = {1, 2, 3, 4, …, 10}. Let R₁ be the relation “is half of” and R₂ be the relation “is the twice of” in the set A. Then;

R₁ = {(1, 2), (2, 4), (3, 6), …, (5, 10)}

R₂ = {(2, 1), (4, 2), (6, 3), …, (10, 5)}

From the above relation, we see that R₂ is the inverse of R₁. Therefore, R₂ = R₁^-1 where R^-1 means inverse relation.

R₂ = R₁^-1 = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5)}

Ex: what is the relation of the following relations;

a) R = {(2, 6), (3, 9), (4, 12)}

b) R = {(1, 0), (4, 1), (7, 2), (10, 4)}

c) “is the parent of”

d) “is less than”

e) “is 1/5 of”

Solution:

1.  R^-1 = {(6, 2), (9, 3), (12, 4)}

b) R^-1 = {(0, 1), (1, 4), (2, 7), (4, 10)}

c) “is the child of”

d) “is more than”

e) “is 5 times of”