Write queries using operations of relational algebra for the questions listed below. Make sure to combine operators together to create more advanced queries to retrieve data. Please clearly mark your answers for each problem.

You may copy and paste the following relational algebra operators in your solution:

$\backslash$sigma $,\backslash$pi $,\backslash$rho $,$ x$,,,,,\backslash$cap $,\backslash$cup $,-,-$:$,$

Use the Subscript option available in the menu when needed.

Given database:

CUSTOMER $($CUST$\_$ID $($PK$),$ CUST$\_$LAST, CUST$\_$FIRST, CUST$\_$PHONE, CUST$\_$EMAIL, CUST$\_$ADDRESS, CUST$\_$CITY, CUST$\_$ZIP, CUST$\_$STATE$)$

ORDERS $($ORDER$\_$NUMBER $($PK$),$ CUST$\_$ID $($FK$),$ PROD$\_$ID $($FK$),$ ORDER$\_$DATE, ORDER$\_$TOTAL$)$

PRODUCT $($PROD$\_$ID $($PK$),$ PROD$\_$DESCRIPTION, PROD$\_$CATEGORY, PROD$\_$PRICE$)$

$1.$ Retrieve City and Email for the customer whose name is John Smith.

$2.$ Retrieve Name and Address of all customers who live in Florida.

$3.$ Retrieve Product Description and Price for the products in the Computer category that cost more than $$100.$

$4.$ Retrieve Product Description and Price for the products in either the Computer or Game category.

$5.$ Retrieve Name and Address of the customers who placed orders on $01-01-2016.$ Note: the CUSTOMER and ORDERS tables are linked through the CUST$\_$ID column.

$6.$ Retrieve Product Description and Price for the products that were purchased on $01-01-2016.$ Note: PRODUCT and ORDERS tables are linked through the PROD$\_$ID column.

$7.$ Retrieve Name and Address of all customers who live in Florida, who purchased product $$TV$.$

$8,9,10.$ Write three more complex queries to retrieve data from these tables. Queries must include multiple conditions and incorporate at least one join, one rename, and one aggregate function operations. All queries must be different. Provide a clear explanation of what each query is intended to do$.$