Show that the relation `R` on 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 and 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 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} .

Let R be the realtion 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 equivalance relation. further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all elements of 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}.

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 multiple of 4} is in equivelance.

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 each case.

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

The relation S={(3,3),(4,4)} on the set A={3,4,5} is

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 defined in the set A of all polygons as R = {(P_(1),P_2):P_1 and P_2 have same number of sides} , is an equivalence relation . What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

If the relation R be defined on the set A = {1,2,3,4,5} by R = {(a,b):|a^(2) -b^(2)| lt 8} . Then , R is given by .............

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.