Translate in two ways each of these statements into logical

Translate in two ways each of these statements into logical expressions using predicates, quantifiers, and logical connectives. First let the domain consist of the students in your class and second let it consist of all people. For instance, for part (a) provide answers labeled (al) for the first domain and labeled (a2) for the second domain. (a) Everyone in your class has a car. (b) Somebody in your class has been in a car crash. (c) There is a person in your class that cannot speak French. (d) All students in your class can swim. (e) Some student in your class does not want a car.

Solution

A1(x) is predicate that x is Student and A2(x) is a predicate that x is everyone.
C(x) - x has a car
F(x) - x cannot speak French
S(x) - x can swin
D(x) - x has met car crash

1) (x : A1)C(x)
(x : A2)(A1(x)->C(x))

2) (x : A1)D(x)
(x : A2)(D(x)) D(x))

4) (x : A1)S(x)
(x : A2)(A1(x)->S(x))