--1:
π Eats.pizza (π name (σ gender = 'female' ∧ age > 20 (Person)) ⨝ Person.name = Eats.name Eats)




--2:
π Serves.pizzeria (σ Serves.price < 10 ((σ name = 'Amy' ∨ name = 'Fay' (Eats)) ⨝ Eats.pizza = Serves.pizza Serves))




--3:

ALLPIZZERIAS = (π Eats.pizza (σ name = 'Amy' (Eats)) ∩ π Eats.pizza (σ name = 'Fay' (Eats))) ⨝ Eats.pizza = Serves.pizza (Serves)

π Serves.pizzeria (σ Serves.price < 10 (ALLPIZZERIAS))




--4:

EatAtDominos = π Frequents.name (σ Frequents.pizzeria = 'Dominos' (Frequents))

PizzasAtDominos = π Serves.pizza (σ pizzeria = 'Dominos' (Serves))

π Eats.name (Eats ⨝ Eats.pizza = Serves.pizza PizzasAtDominos) - EatAtDominos





--5.

OlderThanThirty = π Person.name (σ Person.age > 30 (Person))

PizzeriasServeOlder = π Serves.pizzeria (π Eats.pizza (Eats ⨝ Eats.name = Person.name OlderThanThirty) ⨝ Eats.pizza = Serves.pizza Serves)

YoungerThanThirty = π Person.name (σ Person.age < 30 (Person))

PizzeriasServeYounger = π Serves.pizzeria (π Eats.pizza (Eats ⨝ Eats.name = Person.name YoungerThanThirty) ⨝ Eats.pizza = Serves.pizza Serves)

PizzeriasServeOlder - PizzeriasServeYounger




--6.

NamesOfMushroom = π Eats.name (σ Eats.pizza = 'mushroom' Eats)

ByAge = π Person.age (τ Person.age desc (Person ⨝ Person.name = Eats.name NamesOfMushroom))

ByAge



--7.

PizzeriasVisitedFemale = π Frequents.pizzeria (Person ⨝ Person.gender = 'female' ∧ Person.name = Frequents.name Frequents)

PizzeriasVisitedMale = π Frequents.pizzeria (Person ⨝ Person.gender = 'male' ∧ Person.name = Frequents.name Frequents)

OnlyMale = PizzeriasVisitedMale - PizzeriasVisitedFemale

OnlyFemale = PizzeriasVisitedFemale - PizzeriasVisitedMale

OnlyMale ∪ OnlyFemale





--8.

PizzeriasServePepperoni = σ Serves.pizza = 'pepperoni' Serves

Ordered = τ Serves.price PizzeriasServePepperoni

MinPrice = γ min(Serves.price) -> minPrice (Ordered)

π Serves.pizzeria (Serves ⨝ Serves.price = minPrice MinPrice)