Step 1: Analyzing Statement I.
Statement I says \( 5 + 8 = 12 \) or 11 is a prime. Clearly, \( 5 + 8 = 13 \), not 12. Therefore, this statement is false.
Step 2: Analyzing Statement II.
Statement II says that the Sun is a planet or 9 is a prime. The Sun is not a planet, but 9 is not a prime number, since it is divisible by 3. Therefore, this statement is also false.
Step 3: Conclusion.
Thus, the correct answer is (4) Statement I is false and Statement II is true.