Let `A={1,2,3,ddot,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 `AxAdot` Prove that `R` is an equivalence relation. Also obtain the equivalence class [(2,5)].

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 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 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)] .

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)].

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 A={1,2,3,4} . Let R be the equivalence relation on AxxA defined by (a,b)R(c,d) iff a+d=b+c . Find {(1,3)} .

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 S={1,2,3,4,5} and A=S xx.A relation R on A is defined as follows '(a,b)R(c,d) iff ad=cb. Then R is

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