Show that the relation `R` on the set `A{xZ ;0lt=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 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 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 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 Z of integers,given by R={(a,b):2 divides a-b}, is an equivalence relation.

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even }, is an equivalence relation.

Prove that the relation R in the set A={1,2,3,4,5,6,7} given by R={(a,b):|a-b|iseven} is an equivalence relation.

Prove that the relation R is the set A= {5,6,7,8,9,10} given by R= {(a, b) : |a - b| is divisible by 2} is an equivalence relation. Find the all elements related to the element 6.

Show that the relation R on the set A={1,2,3,4,5}, given by R={(a,b):|a-b| is even }, is an equivalence relation.Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other.But,no element of {1,3,5} is related to any element of {2,4} .

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 the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?