Please answer this question about relations, THANK YOU.

Question: A store is performing inventory and notes unique items in a set, S. Upon conclusion, it is determined that S contains 150 elements, in other words the store offers 150 unique items. Each element of S is given an identification code of nine digits. Part A: Let A be a set made up of the identification code given to some element in S. As some items may have codes with repeating numbers, different sets A will potentially have different lengths depending on the item. Define a relation, say R, based on S. Define two items for R to be related, say s, and S. If the sets A belonging to the two items are the same size, we can write sRs;. Determine if this is an equivalence relation. Please explain why or why not. Part B: Define another relation, say R,, based on S. Define two items for R, to be related, say s," and "=;". If the two items both fit into at least two of the same categories (item descriptions like: cheap, small, new, on sale, etc.), we can write sRs. Determine if this is an equivalence relation. Please explain why or why not