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 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 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 T be set of all triangle in the Euclidean plane , and let a relation R on T be defined as aRb if a is congruent to b,AA "a",b inT . Then, R is ....

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

Show that the relation R in the set A of all the books in a library of a college , given by R = {(x,y) : x and y have same number of pages} is an equivalence relation.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

Show that the relation R defined in the set A of all triangles as R = {(T_(1),T_(2)}T_(1) is similar to T_2 } , is equivalence relation . Consider three right angle triangles T_1 with sides 3,4,5 , T_2 with sides 5,12, 13 and T_3 with sides 6, 8, 10 . Which triangles among T_1 , T_2 and T_3 are related ?