Consider a set S= (5, 10, 12, 13, 15, 18) and d = 30. Solve it for obtaining sum of subset.

Please give me correct solution.

Given set A = {1,2,{3},4,5,{1,2},7}, the possible subsets of set A are {1,2,3,4,5,1,2,7} {1, 2, {3}} {1,2,1,2,1,2,1,2}

Prove that equivalences of sets are transitive, for example if X ~ Y and Y ~ Z then X ~ Z.

On S = f2; 4; 6; 10; 12; 20; 30; 60g we work with the divisibility relation R:xRy , x divides y:(i) Draw the Hasse diagram of R.(ii) Find all R-minimal elements.(iii) Find all R-maximal elements.(iv) Find all non-empty subsets U  S, so that 6 is an R-lowerbound of U.(v) Let A = f6; 10; 12g. If A admits an R-supremum,  nd it. If A admits an R-in mum,  nd it.(vi) Is R a lattice?