[" 8.Show that relation "R" in set "N times N" given by "],[={(a,b)R(c,d)rArr a+d=b+c}" is an "],[" equivatence relation."]

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

Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a+d=b+c is an equivalence relation.

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

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.

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

Prove that the relation R on the set N xx N defined by (a,b)R(c,d)a+d=b+c for all (a,b),(c,d)in N xx N is an equivalence relation.Also,find the equivalence classes [(2, 3)] and [(1,3)].

Prove that a relation R defined on N xx N where (a,b)R(c,d)hArr ad=bc is an equivalence relation.

Show that the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?

Let N be the set of all natural numbers. Let R be a relation on N xx N , defined by (a,b) R (c,c) rArr ad= bc, Show that R is an equivalence relation on N xx N .

If R is a relation in N xx N , show that the relation R defined by (a, b) R (c, d) if and only if ad = bc is an equivalence relation.