Two dice are thrown. Defined are the following two events A and B:
\[
A = \{(x, y) : x + y = 9\}, \quad B = \{(x, y) : x \neq 3\},
\]
where \( (x, y) \) denote a point in the sample space.
Check if events \( A \) and \( B \) are independent or mutually exclusive.