Consider the following schemas for a database used by a share price information system. Table shares ISIN symbol name issuedate date char(12) varchar(6) varchar(25) Table prices symbol varchar(6) date date price integer volume integer Shares are traded on stock market using a "ticker symbol" (the symbol attribute). But the actual share is identified by an ISIN number. The ISIN number can change from time to time (due to share splits etc.). The prices table gives the number of shares of a particular ticker symbol traded on each day and the average price. (a) Write a relational algebra expression for the following problem: Find the ISIN's of stocks that traded over 1,000 shares in any single day in 2021. [4 marks] (b) Write a relational algebra expression for the following problem: Find the ISIN's of stocks that traded over 1,000 shares everyday in 2021. [5 marks] Hint: You may find the following logical equivalence useful in devising your solution: for all x, P not (exists x such that not P) (c) Define precisely what it means for a decomposition of a table into two tables to be lossless decomposition. [1 mark]