Consider the following Schema:

User $($UserId$,$ Name, Password$)$

Patent $($PatentNo$,$ PatentTitle, PatentContents, Diagrams, UserId $($Foreign Key$))$

Bid $($BidNo$,$ UserId $($Foreign Key$),$ PatentNo $($Foreign Key$),$ StartBid, FinalSellingPrice$)$

Give an expression in the relational algebra to express each of the following queries:

i$)$ Find all the bids that started at a price greater than $3000$ and finally sold at less than

$15,000.$

ii$)$ Find the patent no$.$ and patent titles for all the users who sold their patents at a price

greater than $2000.$

Find the output for the following:

$\backslash$Pi $($PatentNo$,$ PatentContents$)(\backslash$sigma $($StartBid $>3000^$ PatentNo $=(\backslash$Pi PatentNo$($Patent$)))$

Bid$)$

Write a sentence describing what the query will return.

Example: All patent holders whose names are John.