The relation on the set `A={x|x|<3,x,in Z}` is defined by `R={(x,y);y=|x|,x!=-1},` Then the numbers of elements in the power set of `R` is

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Show that the relation R on the set A={x in Z;0<=x<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

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

Prove that the relation R on the set A={a in ZZ:1 |x-y| is a multiple of 4} is an equivalence relation. Find also the elements of set A which are related to 2.

Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

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 an equivalence relation. Find the set of all elements related to 1 in each case.

Show that the relation S in the set A={x\ \ Z\ :0\ lt=x\ lt=12} given by S={(a , b):\ a ,\ b\ \ Z ,\ \ |a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.

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 a multiple of 4} is an equivalec relation. Find the set of all elements related to 1 in each case.