Let R be a relation on `N xx N` defined by (a,b) `R(c, d) hArr a + d= b + c` for all `(a,b) (c,d) in N xx N` show that,
(a, b) R (a,b) for all `(a, b) in N xx N`

Let R be a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a,b) R (c, d) rArr (c, d) R (a, b) for all (a, b) (c, d) in N xx N

S is defined on N xxN by ((a,b) , (c,d) in S hArr a +d = b +c ........

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)].

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

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R

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 R be a relation from N to N defined by R={(a,b): a, b in N and a=b^(2)). Are the following true? (i) (a,a) in R," for all " a in N (ii) (a,b) in R," implies "(b,a) in R (iii) (a,b) in R, (b,c) in R" implies "(a,c) in R . Justify your answer in each case.

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.

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