Suppose we have a database for a library system composed of the following relations;

Library $($library#$,$ library name, library address $)[$the key is $($library#$)]$

Reader $($reader#$,$ reader name, reader type, reader address$)[$the key is reader#$]$

Document $($document#$,$ document title, document type, document descriptors$)[$the key is $($doc$-$ ument#$)]$

Copy $($document# $,$copy#$,$ library#$,$ copy location, copy status$)[$the key is $($document#$,$ copy#$)],$ copy status can be $$available$$or $$borrowed$$

Borrowing $($reader#$,$ document#$,$ copy#$,$ date borrowed, date returned$)[$the key is $($document#$,$ copy#$,$ date borrowed$)]$

Express the following queries in Algebra $(1$ to $4),$ Calculus $(2$ and $3),$ SQL $($all$)$

$\backslash$pi $\backslash$sigma $\backslash$rho $=!=-$: $\backslash$cap $\backslash$cup $$

$1.$ List all the document copies, along with the library that has them $($document#$,$ copy#$,$ library#$,$ copy location$).$

$2.$ List the documents that the reader $$John$$ has.

$3.$ List the documents not available in any library.

$4.$ List the documents available in every library.

$5.$ Which document is the most borrowed?