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.

Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.

Check whether the relation R defined in the set {1, 2,3,4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

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 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.

Check whether the relation R defined in the set (1, 2, 3, 4, 5, 6) as R= {(a, b) : b = a +1)} is reflexive, symmetric or transitive ?

If R is a relation on the set S = {1,2,3,4,5,6,7,8,9) given by xR y ,y = 3x, then R = is