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`

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 .

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

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 S be the set of all real numbers and Let R be a relations on s defined by A R B hArr |a|le b. then ,R is

Let N be the set of all natural numbers. Let R be a relation on N xx N , defined by (a,b) R (c,c) rArr ad= bc, Show that R is an equivalence relation on N xx 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) 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 A=NxxN , and let * be a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a d+b c ,\ b d) for all (a ,\ b),\ (c ,\ d) in NxxNdot Show that A has no identity element.

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 X Z_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

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)].

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)].