For illustration, consider a relation R in the set A = {1, 2, 3, 4} given by
R = {(a, b): a – b = 10} This is the empty set, as no pair (a, b) satisfies the condition
a – b = 10 Similarly, R′ = {(a, b) : | a – b | ≥ 0} is the whole set A × A, as all pairs
(a, b) in A × A satisfy | a – b | ≥ 0 These two extreme examples lead us to the
following definitions