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

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 on 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?

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?

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

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

Show that the relation ‘is congruent to’ on the set of all triangles in a plane is an equivalence relation

Show that each of the relation R in the set A={x in Z :0lt=xlt=12} , given by(i) R = {(a , b) : |a - b| is a multiple of 4} (ii) R = {(a , b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Show that the relation R on the set A of points in a plane, given by R={(P ,\ Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0,\ 0) is the circle passing through P with origin as centre.

Show that the relation R on the set A of points in a plane, given by R={(P ,\ Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further show that the set of all points related to a point P!=(0,\ 0) is the circle passing through P with origin as centre.

Let R be a relation on the set of all real numbers defined by xRy iff |x-y|leq1/2 Then R is