We have designed an eBay-like on-line auction database. Please use relational algebra to write queries in order to obtain the requested information. (Note: Every auction listed in the system, sold, expired, or ongoing, is listed in Auction table. Auctions, whose items have been sold out, are also listed in Sold table.)

Item (ItemID, ItemName, Description)

User (Username, Email, Rating)

Auction (AuctionID, ItemID, SellerUsername, Price, StartTime, EndTime)

Sold (AuctionID, BuyerUsername, DateSold)

1. Find usernames of the users who have a rating higher than 4.5;

2. Find a distinct list of usernames of the users who participate in an auction. Note that a user may participate in an auction as either a buyer or a seller;

3. Find a list of usernames of the sellers whose items have been sold;

4. Find a list of AutionIDs for the auctions that have been expired. (Hint: An expired auction is the one whose item is not sold and EndTime < CurrentTime. You can use CurrentTime in the query to indicate the current system time.);

5. Find the ItemName of the highest priced item, along with the Username of the corresponding user selling the item. Note that there may be more than one item at the highest price, in which case, you must