To determine whether the statement is true or false, we need to understand the role of counterexamples in mathematical logic. A statement is typically a universal claim that asserts something to be true for all cases within a certain context. For example, a statement might claim that all swans are white.
A single counterexample is enough to prove that a universal statement is false. If we can find just one case where the statement does not hold, then it cannot be true for all cases. For instance, if we find a black swan, we have effectively disproven the claim about all swans being white.
Therefore, the assertion that ‘two counterexamples are needed to prove a statement is false’ is false. In conclusion, one counterexample is sufficient to demonstrate that a universal claim is not valid.