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

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)].

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

Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ d) a+d=b+c for all (a ,\ b),\ (c ,\ d) in NxxN 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 NxxN , defined by (a ,\ b)R\ (c ,\ d) a d=b c for all (a ,\ b),\ (c ,\ d) in NxxN . Show that R is an equivalence relation on NxxN

If R is a relation on NxxN defined by (a,b) R (c,d) iff a+d=b+c, then

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 Z be the set of all integers and Z_0 be the set of all non-zero integers. Let a relation R on ZxxZ_0 be defined as follows: (a ,\ b)\ R\ (c ,\ d)hArra d=b c for all (a ,\ b),\ (c ,\ d) in ZxxZ_0 Prove that R is an equivalence relation on ZxxZ_0

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let Z be the set of all integers and Z_0 be the set of all non-zero integers. Let a relation R on ZxxZ_0 be defined as follows: (a , b)R(c , d) if and only if a d=b c for all (a , b),(c , d) in ZxxZ_0 Prove that R is an equivalence relation on ZxxZ_0 .

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