4. Let Q = {9192.. qnen > 3 and qi {0, 1, 2, 3} for i =1,2,...,n}, i.e. the set of quarternary strings of length three or more. Let R be a relation on such that vRw if and only if vi+U2 = wi+wz and v3 = w; (with the convention that I; represents the jth digit of the string r). Prove that Ris an equivalence relation