Let L denote the set of all straight lines in a plane. Let a relation R be defined by ℓ R m iff ℓ is perpendicular to m for all ℓ, m ϵ L. Then, R is

The maximum number of equivalence relations on the set A = {1, 2, 3} is

Let R be a relation on the set N of natural numbers defined by n R m iff n divides m. Then, R is

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a R b if a is congruent to b for all a, b ϵ T. Then, R is

Consider a non-empty set consisting of children in a family and a relation R defined as a R B if a is brother of b. Then, R is