Final answer:
The negation of the statement 'If a computer program P compiles without error messages, then P is correct' is 'a computer program P such that P compiles without error messages but P is not correct.' This asserts that successful compilation does not guarantee program correctness.
Step-by-step explanation:
The original statement is 'If a computer program P compiles without error messages, then P is correct.' The negation of this statement would be a new statement that if the original one is true, the negation would be false, and vice versa. In logic, we affirm a negation by asserting that it is not the case that if 'P then Q' is true, it is possible to have 'P and not Q'. Therefore, the correct negation would be 'a computer program P such that P compiles without error messages but P is not correct.' This means that even if the program compiles successfully (without errors), it might still not be a correct program in terms of doing what it's supposed to do functionally or logically.