[" b) "R" in "A={x in Z|0<=x<=12}" given by "],[R={(a,b)/|a-b|" is a multiple of "4}],[" c) "R" in "A={x in N/x<=10}" given by "],[R={(a,b)|a-b}]

Show that the relation R in the set A = {x in Z : 0 le x le 12} given by R = {a , b) : |a - b| is a multiple of 4} is an equivalence relation.

Show that the relation R in the set A={x in z, 0 le x le 12} given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.

Show that each of the relation R in the set A = { x in Z : 0 le x le 12} given by R = {(a,b):|a-b| is multiple of 4} is in equivelance.

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b): a = b} are equivalence relations.

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : R.

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : domain of R.

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : range of R.

If a, b,c> 0 and x,y,z in R then the determinant: |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to