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

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} .

Interval form of the set { x in R | -1 le x lt 7 } is given by (-1, 7] .

Show that the relation R in the set A of all the books in a library of a college , given by R = {(x,y) : x and y have same number of pages} is an equivalence relation.

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 ?

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

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.

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L_(1),L_2} : L_(1) is parallel to L_2 } . Show that R is an equivalence relation . Find the set of all lines related to the line y = 2x + 4.