Let A = {3,5} and B = {7, 11}. Let `R = {(a, b):a in A, b in B, a -b` is odd}. Show that R is an empty relation from A into B.

Let A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8, 10}. Let R = {(a, b): a in A, b in B , a divides b} be a relation from A into B. Find R. Show that domain of R is A and range of R is B.

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}.

Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine : Is A xx B= B xx A ?

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 A={a,b,c} and B={1,2,3}. Find the number of relations from A into B.

Let A= {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}. Find : A - B and B - A. Show that A- B ne B-A .

Let R be a relation from Q to Q defined by : R = {(a, b): a,b in Q and a-b in Z }. Show that : (a, a) in R for all a in Q.

Let A = {1,2,3,4} and B= {x,y,z}. Consider the subset R = {1, x), (1,y),(2,z),(3,x)} of A xx B . Is R, a relation from A to B? If yes, find domain and range of R. Draw arrow diagram of R.

Let R be a relation from a set A to a set B, then:

Let a * b = a + 2b - 5 , find 3 * 5