Let `A={1,2,3}" and define" R={(a,b):a-b=12}`. Show that R is empty relation on Set A.

Let A={1,2,3} and define R={(a,b):a+b gt 0} . Show that R is a universal relation on Set A.

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 and B.

Let A={3,5}" and "B={7,9}. Let R={(a,b):a in A,b inB" and "(a-b)" is odd"}. Show that R is an empty relation from A to B. Hint The difference of two odd numbers cannot be odd.

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 relations from A into B.

Let S be the set of all real numbers and let R be a relation in s, defined by R={(a,b):aleb}. Show that R is reflexive and transitive but not symmetric .

Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

Let A={1, 5), B={3, 7) and R={(a, b) :a in A, b in B and a-b is a multiple of 4}. Show that R is an empty relation from A to B.

Let R be a relation on a set A = {1,2,3,4,5} defined as R = { (a,b) : | a ^(2) - b ^(2)| lt8}. Then the reation R is

Let A = {1, 2, 3} and R = {(a,b): a,b in A, a divides b and b divides a}. Show that R is an identity relation on A.

Let S be the set of all real numbers and let R be a relation in s,defined by R={(a,b):aleB^(2)}. show that R satisfies none of reflexivity , symmetry and transitivity .