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.