Show that relation `R = {(L_1, L_2) : L_1` is parallel to `L_2`}, defined on the set of all lines, is an equivalence relation.

Show that relation R = {(T_1, T_2) : T_1 is similar to T_2 }, defined on the set of all triangles, is an equivalence relation.

Let a relation R ={(L_1, L_2) : L_1 is perpendicular to L_2} , be defined on the set of all lines L in a plane. Show that R is symmetric metric but neither reflexive nor transitive.

Show that relation R = {(P_1, P_2) : P_1 and P_2 have same numbers of sides}, defined on the set of all polygons is an equivalence relation

The relation ‘is parallel to’, on the set A of all coplanar straight lines is an equivalence relation.

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 L be the set of all lines in XY-pJane 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 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 equilavence relation.

If relation R defined on set A is an equivalence relation, then R is

Let L be the set of all lines in the XY-plane and R be the relation in L defined by : R = {(l_i l_j) = l_i is parallel to l_j. Aai,j} Show that R is an equivalence relation. Find the set of all lines related to the y = 7x +5.

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.