Let L be the set of all lines in a plane and R be the relation in L defined as `R = {(L _(1), L _(2)) : L _(1)` is perpendicular to `L _(2)` }. Show that R is symmetric but neither reflexive nor transitive.

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L _(1) , L _(2)) : L _(1) is parallel to L _(2)}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x +4.

Let T be the set of all triangles in a plane with R a relation in T given by R ={(T _(1) , T _(2)): T _(1) is congruent to T _(2) } Show that R is an equivalence relation.

Let T be the set of all trianges 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 in T Then R is

Show that the relation R in the set {1,2,3} given by R = {(1,2), (2,1) is symmetric but neither reflexive nor transitive.

Show that the relation S in the set R of real numbers defined as S={(a,b): a, b in R and a le b^(3) } is neither reflexive, nor symmetric, nor transitive.

Let R be the relation over the set of straight lines in a plane such that l R m iff l bot m . Then R is :

Prove that the relation R defined on the set of real numbers R as R = {(a,b) : a le b^(2) AA a, b in R} is neither reflexive nor symmetric nor transitive.

Show that the relation R in R defined R = {(a, b) : a le b} is reflexive and transitive but not symmetric.

Let L be the set of all straight lines in the Euclidean plane. Two lines l_(1)" and "l_(2) are said to be related by the relation R" iff "l_(1) || l_(2) . Then the relation R is :