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: AiRAjsum(Ai) = sum(Aj) where A, and A, are elements of A, and sum(At) denotes the sum of all elements of A, so, for example.(37) and { 1,2,3,4) are in relation R because 3+7=1+2+3+4. Observe that R 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? Explain why