Discrete Mathematics

Question

Let N(x) be the statement "x has visited Finland," where the domain consists

of the students in your school. Express each of these quantifications∋ in English.

(a) ∃xN(x)

(b) ¬∃xN(x)

(c) ∃x¬N(x)

(d) ¬∀xN(x)

Answer 1

Let N(x) be the statement "x has visited Finland," where the domain consists

of the students in your school. Express each of these quantifications∋ in English.

(a) ∃xN(x)

(b) ¬∃xN(x)

(c) ∃x¬N(x)

(d) ¬∀xN(x)

∃x means there exists an x that makes N(x) true

¬∃x means there does not exist an x that makes N(x) true

¬N(x) means that N(x) is not true.

∀x means that N(x) is true for all x

¬∀x means that "N(x) is true for all x" is not true.

a) At least one student in your school has visited Finland.

b) No student in your school has visited Finland

c) There is a student in your school who has not visited Finland

d) Not all the students in your school have visited Finland.