Final answer:
The set representing all integers except 19 is x , which correctly limits the elements to integers that are not equal to 19.
Step-by-step explanation:
The set that represents all integers except for 19 is x . This notation is saying that the set includes all elements x such that x belongs to the set of integers (ℤ symbolizes the set of all integers) and at the same time, x is not equal to 19. Therefore, the correct answer to the question is (c) x ∈ ℤ and x ≠ 19. Answer choices (a) and (b) do not specifically restrict x to be an integer, and answer choice (d) is incorrect due to being a duplicate and possibly a typographical error within the question itself.