Expressions with several quantifiers
Let the universe of discourse be the set of all Students (of VU).
Let C(x) mean “x has a computer”, and F(x,y) mean “x and y
are friends”. Translate the following into English:
--- Every student has a computer
--- There is a student who has no friends
- ?x[C(x) ? ?y(F(x,y) ? C(y))]
--- Every student has a computer
or has a friend with a computer
- How to say that there is a student who has (at least) 2 friends?
--- ?x ?y ?z (F(x,y) ? F(x,z))
?x ?y ?z (F(x,y) ? F(x,z) ? y?z))
- How to say that there is a student who has exactly 2 friends?
--- ?x ?y ?z (F(x,y) ? F(x,z) ? y?z ? ?t (F(x,t) ? (t=y ? t=z)))