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import database$($found below$)$ on RelaX and do the following

Write the relational algebra expression for the following queries using the syntax on RelaX.

Provide the output of the expression $($schema of the table and content$).$

Verify the solution on Relax.

Person$($name$,$ age, gender$)//$ name is PK

Frequents$($name$,$ pizzeria$)//[$name$,$pizzeria$]$ is PK

Eats$($name$,$ pizza$)//[$name$,$pizza$]$ is PK

Serves$($pizzeria$,$ pizza, price$)//[$pizzeria$,$pizza$]$ is PK

a$.$ Find all pizzerias frequented by at least one person under the age of $20.$

b$.$ Find all pizzas eaten by at least one female over the age of $22.$

c$.$ Find pizzerias frequented by teenagers eating mushroom or pepperoni. $($A teenager is a person of age $13-19).$

d$.$ Find pizzerias frequented by teenagers eating mushroom and pepperoni.

e$.$ Find the names of all females who eat at least one pizza served by Mod Pizza.

f$.$ Find all pizzerias that serve at least one pizza for less than $$10$ that both Amy and Fay eat.

g$.$ Find the names of all people who eat at least one pizza served by Dominos but who do not frequent Dominos.

h$.$ Find all pizzas that are eaten only by people younger than $24,$ or that cost less than $$11$ everywhere they're served.

i$.$ Find the age of the youngest person $($or people$)$ who eat pepperoni pizza.

j$.$ Find all pizzerias that serve pizzas only eaten by people over $29.$

k$.$ Find all pizzerias that serve every pizza eaten by people over $29.$

l$.$ Find all pizzerias that serve the cheapest cheese pizza.

m$.$ Find all pizzerias exactly serving only two pizzas.

Database:

group: pizzas

Person $=\{$

name:string, age:number, gender:string

Amy, $16,$ female

Ben, $21,$ male

Cal, $33,$ male

Dan, $13,$ male

Eli, $45,$ male

Fay, $21,$ female

Gus, $24,$ male

Hil, $30,$ female

Ian, $18,$ male

$\}$

Eats $=\{$

name:string, pizza:string

Amy, mushroom

Amy, pepperoni

Ben, cheese

Ben, pepperoni

Cal, supreme

Dan, cheese

Dan, mushroom

Dan, pepperoni

Dan, sausage

Dan, supreme

Eli, cheese

Eli, supreme

Fay, mushroom

Gus, cheese

Gus, mushroom

Gus, supreme

Hil, cheese

Hil, supreme

Ian, pepperoni

Ian, supreme

$\}$

Frequents $=\{$

name:string, pizzeria:string

Amy, "Pizza Hut"

Ben, "Papa Jones"

Ben, "Pizza Hut"

Cal, "Christians Pizza"

Cal, "Mod Pizza"

Dan, "Christians Pizza"

Dan, "Mod Pizza"

Eli, "Papa Jones"

Eli, "Mod Pizza"

Fay, "Dominos"

Fay, "Little Caesars"

Gus, "Papa Jones"

Gus, "Pizza Hut"

Hil, "Dominos"

Hil, "Pizza Hut"

Hil, "Mod Pizza"

Ian, "Dominos"

Ian, "Christians Pizza"

Ian, "Mod Pizza"

$\}$

Serves $=\{$

pizzeria:string, pizza:string, price:number

"Papa Jones", cheese, $7\mathrm{.}75$

"Papa Jones", supreme, $8\mathrm{.}5$

"Dominos", cheese, $9\mathrm{.}75$

"Dominos", mushroom, $11$

"Little Caesars", cheese, $7$

"Little Caesars", mushroom, $9\mathrm{.}25$

"Little Caesars", pepperoni, $9\mathrm{.}75$

"Little Caesars", sausage, $9\mathrm{.}5$

"Christians Pizza", cheese, $7$

"Christians Pizza", pepperoni, $8$

"Christians Pizza", supreme, $8\mathrm{.}5$

"Pizza Hut", cheese, $9$

"Pizza Hut", pepperoni, $12$

"Pizza Hut", sausage, $12$

"Pizza Hut", supreme, $12$

"Mod Pizza", cheese, $9\mathrm{.}25$

"Mod Pizza", pepperoni, $8$

"Mod Pizza", sausage, $9\mathrm{.}75$

$\}$