Consider the following statement.

$AA$ computer program $P,$ if $P$ compiles without error messages, then $P$ is correct.

Which of the following is a negation for the statement?

$EE$ a computer program $P$ such that $P$ compiles with error messages and $P$ is not correct.

$AA$ computer program $P,$ if $P$ compiles without error messages, then $P$ is not correct.

$EE$ a computer program $P$ such that $P$ compiles without error messages but $P$ is not correct.

$AA$ computer program $P,$ if $P$ compiles with error messages, then $P$ is not correct.

$EE$ a computer program $P$ such that $P$ compiles with error messages but $P$ is correct.