Show that the relation R defined in the set A of all triangles as : `R = [(T_1, T_2): T_1 and T_2` are similar triangles} is an equivalence relation .

Show that the relation R, defined by the set A of all triangles as : R = { (T_1, T_2) = T_1 is similar to T_2} is an equivalence relation. Consider three right-angled triangles T_1 with sides 3, 4, 5, T_2 with sides 5, 12, 1 3 and T_3 with sides 6, 8, 10.

Show that the relation R defined in the set A of all lines as R = {(L_1, L_2): L_1 and L_2 are parallel lines} is an equivalence relation.

Show that the relation R defined in the set A of all polygons as : R = {(P_1, P_2) : P_1 and P_2 have same number of sides} is an equivalence relation.

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

Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number of sides} , is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b) : |a - b| is a multiple of 4} 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 R be the relation defined on the set : A= {1, 2, 3, 4, 5,.6, 7} by: R ={(a, b) : a and bare either odd or even}. Show that R is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.