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 . 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 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.

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 ?

Show that each of the relation R in the set A = { x in Z : 0 le x le 12} given by R = {(a,b): a = b } is an equivalence relation . Find the set of all elements related to 1 each case.

The relation R is defined on the set of natural numbers as {(a,b): a = 2b}, the R^(-1) is given by

The relation R defined in the set of real number R is as follow : R {(x,y) : x - y + sqrt2 is an irrational number} Is R transitive relation ?

The maximum number of equivalence relations on the set A = {1,2,3} are ..........

The relation R defined on the set of natural numbers as {(a,b) : a differs from b by 3} is given by

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.

Show that the relation R in the set A = {1,2,3,4,5} given by R {(a,b) : |a-b| is even } , is an equivalence relation . Show that all the elements of {1,3,5} are related to each other all the elements of {2,4} are related to each other . But no element of {1,3,5} is related to any element of {2,4} .