List all the relations on the set A = {0,1}.

List all the subsets of the set {- 1, 0, 1}.

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 in each case.

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 a multiple of 4} is an equivalec relation. Find the set of all elements related to 1 in each case.

Let R = {(1, 3), (4, 2), (2, 4), (2, 3) (3, 1)} be a a relation on the set A = {1, 2, 3, 4}. The relation R is :

Fill in the blank: Consider the set A = (0,1,2) and let R = (0,1), (1,0) be the relation on A, then R is a _________ relation on A.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

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} are equivalence relations.

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}.