[Database Systems] please show all work.

Consider a relation Stocks (B, O, I, S, Q, D, M, L) , whose attributes may be thought of informally as broker , office ( of the broker ) , investor , stock , quantity( of the stock owned by the investor ) , dividend ( of the stock ), market (markets the stock is listed in, stock can be listed in many markets) and location (location of market). Let the set of FD ' s for Stocks be S --> D, I --> B, IS --> Q, B --> O and M --> L.

Use the 3 NF synthesis algorithm to find a lossless- join, dependency - preserving decomposition of Stocks into 3 NF relations.