Which of the following relations R on sets A are equivalence relations? Which are partial orders? For those that are equivalence relations, what is A/R? For those that are partial orders, what are the minimal and smallest elements, if any?

(a) A = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, R = {(a, b) A Aa and b have the same number distinct prime factors}

(b) A = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} R = {(a, b) A Aa divides b}

(c) A = {2, 5, 10, 30, 100, 1000, 2000} R = {(a, b) A Aa has the same number of digits as b or more digits than b}

(d) A = {2, 5, 10, 30, 100, 1000, 2000} R = {(a, b) A Aa has the same number of digits as b}