Final answer:
Without the full statement regarding every integer x, it is impossible to select a definitive counter-example from the provided options. However, the number 0 is often a special case in mathematical statements and could potentially serve as a counter-example depending on the specific claim.
Step-by-step explanation:
The question asks for a counter-example to the statement that for every integer x, x [...] (since the statement is incomplete, we're missing the full context of what's being claimed about every integer x). Given the choices provided, the goal is to find a value of x among -1, 0, 1, and 2 that would disprove a supposedly false universal claim. As the full claim is not presented, it's essential to understand the nature of counter-examples in mathematics. A counter-example is a single instance that shows a statement to be false. For example, if a statement claims that all integers have a certain property, finding just one integer that does not possess that property would suffice to disprove the statement.
However, without the complete statement, we cannot definitively select a counter-example. In mathematical practice, the number 0 often serves as a unique case that can defy certain properties that hold for all other integers. For instance, if the implicit claim involves division or multiplication properties, zero could be the likeliest choice for a counter-example. Choice (2), which is 0, is often a special case in mathematical statements and is thus a potential counter-example. However, without additional information, this cannot be determined with certainty in this case.
If further context is provided as to what the statement claims regarding every integer x, a clear counter-example could be selected from the given options.