Prove that the relation R defined on the set V of all vectors by `vecaRvecbif veca=vecb,` is an equivalence relation on V.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 5 divides abs(a-b)} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 3 divides abs(a-b)} is an equivalence relation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Define an equivalence relation. Show that the relation similarity on the set of all triangles in a plene is an equivalence relation.

Show thaT the relation R in the set of all integers Z defined by R{(a,b) : 2 divides a-b} is an equivalence relation.

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} is an equivalence relation.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

(i) Prove that the relation ""_(x)R_(y) iff 3 is a factor of (x-y) , defined on the set of integers is an equivalence relation. (ii) If x is the set of real numbers, then prove that the relation R={(a,b): a in x, b in x and a=b} is an equivalence relation.