1. Let A be the set of all (nonempty) subsets of integer numbers between 1 and K (including 1 and K), K>1. Let R be a binary relation on A defined as follows: A'RAj sum(Ai)= sum(Aj) where A, and Aj are elements of A, and sum(Ai) denotes the sum of all elements of Ai, so, for example, 3,7} and 1,2,3,4] are in relation R because 3+7-1+2+3+4. Observe that FR is an equivalence relation on A. (a) What is the number of equivalence classes of R (as a function of K)? Explain why. (b) Assume K 10. List all subsets in the equivalence class which contains 10 (c) How many equivalence classes contain just one element? What are these classes? Explairn why