logic basics

Question

Translate in 2 ways each of these logical expression using predicate quantifiers and logical connectives

First take domain as student in your class

Second : let the domain be all people

a) Every body in your class has cellular phone     :

b)  Somebody in your class has seen a foreign movie   

c) There is a person in your class who cannot swim    

d) All student in your class can solve quadratic equation  

e) Some student in your class does not want to be rich

Answer 1

just verify domain : student in your class

a) Every body in your class has cellular phone :∀x(C(x)) where C (x) mean x has cellular phone

b) Somebody in your class has seen a foreign movie ∃x(M(x)) where M(x) : x has seen a movie

c) There is a person in your class who cannot swim ∃x(∽S(x)) where S(x) mean x can swim

d) All student in your class can solve quadratic equation ∀x(Q(x) where Q(x) mean x can solve quadratic equation

e) Some student in your class does not want to be rich ∃ x(∽R(x)) R(x) : x  want to be rich

For second when the domain is set of all people

Let Cc(x) - X is in your class

a) :∀x(Cc(x) --->C(x))

b) ∃x(Cc(x) ∧M(x))

c) ∃x(Cc(x) ∧ ∽S(x))

d) ∀x(Cc(x) --->Q(x))

e) ∃x(Cc(x) ∧ ∽R(x))