[" (b) "1],[" 9.The relation 'R' in "N times N" such that "(a,b)" R "(c,d)hArr a+d=b+c" is "]

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

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

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 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.

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

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.

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.

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 union of two equivalence relations is an equivalence relation.