Let S be the set of all points in a plane and R be a relation on S defines as `R={(P,Q):` distance between `P and Q` is less than 2 units} Show that R is reflexive and symmetric but not transitive.

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 S be the set of all real numbers and Let R be a relations on s defined by A R B hArr |a|le b. then ,R is

Let a relation R_1 on the set R of real numbers be defined as (a , b) in R iff 1+a b >0 for all a , b in Rdot Show that R_1 is reflexive and symmetric but not transitive.

Let a relation R_1 on the set R of real numbers be defined as (a ,\ b) in R_1 1+a b >0 for all a ,\ b in R . Show that R_1 is reflexive and symmetric but not transitive.

Let N be the set of all natural numbers and let R be relation in N. Defined by R={(a,b):"a is a multiple of b"}. show that R is reflexive transitive but not symmetric .

Let A be the set of human beings living in a town at a particular time and R be the relation on A defined by R-{(x ,y) : x is exactly 7cm taller than y} Check whether the relation R is reflexive, symmetric or transitive on A.

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 in T . Then, R is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

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 in L . Then, R is (a) reflexive (b) symmetric (c) transitive (d) none of these

Check whether the relation R in R defined by R={(a ,b):alt=b^3} is reflexive, symmetric or transitive.

Check whether the relation R on R defined by R={(a ,\ b): alt=b^3} is reflexive, symmetric or transitive.