Let sets R and T be defined as
`R = {x in Z|x` is divisible by 2}
`T = {x in Z |x` is divisible by 6}. Then, `T subset R`

Let sets R and T be defined as R= {x in Z|x is divisible by 2} T= {x in Z| x is divisible by 6}. Then T sub R .

Let R be the relation on the set Z of all integers defined by R={(x, y) : x,y in Z,x-y is divisible by n}.Prove that i) (x, x) in R for all x in , Z ii) (x, y) in R implies that (y, x) in R for all x, y in Z iii) (x, y) in R and (y, z) in R implies that (x, z) in R for all x, y, z in Z

Prove that the relation R defined in the set A= { x: x in Z, 0 le x le 12} as R = {(a, b) : abs(a-b) . is divisible by 5} is an equivalence relation.

Prove that the relation R defined in the set A= { x: x in Z, 0 le x le 12} as R = {(a, b) : abs(a-b) . is divisible by 3} is an equivalence relation.

Let R be a relation defined on the set Z of all integers and xRy when x+2y is divisible by 3.then

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 R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation