Question

 Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives.

a) No one is perfect. b) Not everyone is perfect. c) All your friends are perfect. d) At least one of your friends is perfect. e) Everyone is your friend and is perfect. f ) Not everybody is your friend or someone is not perfect.

Answer 1

Solution:

(a) ¬∃x(P (x))

(b) ¬∀x(P (x))

(c) ∀x(F (x) → P (x))

(d) ∃x(F (x) ∧ P (x))

(e) ∀x F(x)∧∀xP(x)

(f) (¬∀x F(x))∧(∃x¬P(x))