Question attached bellow

(08) Let S = {1,2,...,n} and A: P(S) {Q} . In words, the set A consists of all non-empty subsets of S. For each set A e A, let m(A) to be the smallest element of the set A. a) Define a binary relation R ; Ax A such that (A, B) e R 4:) m(A) = m(B). Prove that R is an equivalence relation on A. b) What is the cardinality of the quotient A/ R ? c) Dene a binary relation p on A by: (ALB) e p <:> [A = B v m(A)