Show that the relation R in the set Z of integers given by = {(,y):(x-y)is multiple of 4} is an equivalence relation

Show that the relation R in the set Z of integers given by = {(,y):(x-

1.	Show that the relation R in the set Z of integers given by = {(,y):(x-y)is multiple of 4} is an equivalence relation
Answer» nswerThe relation R on Z is given by R={(a,b):2dividesa−b}AnswerThe relation R on Z is given by R={(a,b):2dividesa−b}We observe the following PROPERTIES of relation RAnswerThe relation R on Z is given by R={(a,b):2dividesa−b}We observe the following properties of relation RReflexivity: for any a∈ZAnswerThe relation R on Z is given by R={(a,b):2dividesa−b}We observe the following properties of relation RReflexivity: for any a∈Za−a=0=0×2AnswerThe relation R on Z is given by R={(a,b):2dividesa−b}We observe the following properties of relation RReflexivity: for any a∈Za−a=0=0×2⇒ 2 divides a−a⇒(a,a)∈RAnswerThe relation R on Z is given by R={(a,b):2dividesa−b}We observe the following properties of relation RReflexivity: for any a∈Za−a=0=0×2⇒ 2 divides a−a⇒(a,a)∈RSo, R is relexive relation on Z