Translate each of these quantifications into English and determine their truth value. [ ∀ x ∈ ℤ, ; (x - 1 ∈ ℤ) ]
a) All integers x such that x - 1 is an integer. b) There exists an integer x such that x - 1 is an integer. c) No integers x such that x - 1 is an integer. d) Some integers x such that x - 1 is not an integer.