These are practice problems for the midterm.  If you need help with
any of them, please come to office hours, or make a separate
appointment.

Schema:

Likes(drinker, beer)
Frequents(drinker, bar)
Serves(bar, beer)

AGGREGATE QUERIES

* for each bar, count the number of drinkers that frequent it, and that like both 'heineken' and 'bud'

* for each bar that serve both 'heineken' and 'bud' count the number of drinkers that frequent that bar

* for each bar that serve 'heineken' count the number of drinkers that frequent that bar and that like 'bud'

EXISTENTIAL AND UNIVERSAL QUANTIFIER

* find all drinkers that frequent some bar that serves some beer that they like

* find all drinkers that frequent only bars that serve some beer that they like

* find all drinkers that frequent some bar that serves only beer that they like

* find all drinkers that frequent some bar that serves some beer that they don't like

* find all drinkers that frequent some bar that serves only beer that they don't like

* find all drinkers that frequent only bars that serve some beer that they don't like

* find all drinkers that frequent only bars that serve only beer that they don't like