Show that the relation R in the set `{1, 2, 3}`given by `R = {(1, 2), (2, 1)}`is symmetric but neither reflexive nor transitive.

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2) ., (2,3)} is reflexive but neither symmetric nor transitive.

Give an example of relation . Which is Symmetric but neither reflexive nor transitive.

The relation R on the set A = {1,2,3} defined as R = {(1,1),(1,2),(2,1),(3,3)} is reflexive , symmetric and transitive.

Show that the relation R in the set R of real number , defined as R = {(a,b) : a le b^2} is neither reflexive nor symmetric nor transitive.

If the relation R on the set {1,2,3} be defined by R = {(1,2)}. Then , R is .........

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 . Show that all the elements of {1,3,5} are related to each other all the elements of {2,4} are related to each other . But no element of {1,3,5} is related to any element of {2,4} .

Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } 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.

Show that the number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is two.