Show that the relation R defined by `(a,b) R (c,d) implies a + d = b +c` on the set `N xxN` is an equivalence relation.

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxNdot

R is relation in N xxN as (a,b) R (c,d) hArr ad = bc . Show that R is an equivalence relation.

Let A = {1,2,3.......9} and R be the relation in AxxA defined by (a,b) R , (c,d) if a + d = b + c for (a,b) , (c,d) in AxxA . Prove that R is an equivalence relation and also obtain the equivalent class [(2,5)].

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.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv= yu. Show that R is an equivalence relation.

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.

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