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

Let A = {3,5}, B = {7,1}. Let R = {(a,b): ainA, binB, a-b is even}. Show that R is an universal relation from A to B.

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 = {3, 5} and B = {7, 11}. Let R = {(a, b) : a in A, b in B, a-b is even} Show that R is an universal relations from A into B.

Let R be the relation on set A={x:x in Z, 0 le x le 10} given by R={(a,b):(a-b) "is divisible by " 4} . Show that R is an equivalence relation. Also, write all elements related to 4.

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 .

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.

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 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 n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot