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.

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.

Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

Let N be the set of all natural numbers and let R be a relation on N xx N, defined by (a,b)R(c,d)ad=bc for all (a,b),(c,d)in N xx N. Show that R is an equivalence relation on N xx N. Also,find the equivalence class [(2,6)].

Let Z be the set of all integers and Z_0 be the set of all non=zero integers. Let a relation R on ZxZ_0 be defined as follows: (a , b)R(c , d) a d=b c for all (a , b),(c , d)ZxZ_0 Prove that R is an equivalence relation on ZxZ_0dot

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

Let Z be the set of all integers and Z_(0) be the set of all non-zero integers.Let a relation R on Z xx Z_(0) be defined as follows: (a,b)R(c,d)hArr ad=bc for all (a,b),(c,d)in Z xx Z_(0) Prove that R is an equivalence relation on Z xx Z_(0)

Let A={1,2,3,......, 12} and R be a relation in A xx A defined by (a, b) R (c,d) if ad=bc AA(a,b),(c,d) in A xx A . Prove that R is an equivalence relation. Also obtain the equivalence class [(3,4)] .

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

Let R be a relation on NxxN defined by (a , b) R(c , d)hArra+d=b+c for a l l (a , b),(c , d) in NxxN show that: (i) (a , b)R (a , b) for a l l (a , b) in NxxN (ii) (a , b)R(c , d)=>(c , d)R(a , b)for a l l (a , b), (c , d) in NxxN (iii) (a , b)R (c , d)a n d (c , d)R(e ,f)=>(a , b)R(e ,f) for all (a , b), (c , d), (e ,f) in NxxN