Question

a. Everyone in your class has a cell phone. b. Somebody in your class has seen a foreign movie. c. There is a person in your class who cannot swim. d. All students in your class can write proofs. e. Some student in your class does not want to be rich.

Answer 1

See below

Explanation:

Your question is incomplete, but probably you want to express each statement with propositional calculus.

Let S be the set of all students of your class. Given a variable x, symbolize the statements:

c(x):="x has a cellphone"

f(x):="x has seen a foreign movie"

s(x):="x can swim"

p(x):="x can write proofs"

r(x):="x wants to be rich"

Remember the quantifiers "There exists (∃)" and "For all (∀)". Using the domain of discourse S and the variable x∈S, we can write the statements as:

a) (∀x)(c(x))

b) (∃x)(f(x))

c) (∃x)(¬s(x))

d) (∀x)(p(x))

e) (∃x)(r(x))