If E and F are independent events, prove or disprove that E and F are necessarily independent

Question:

If E and F are independent events, prove or disprove that E and F are necessarily independent events. In Exercises 18, 20, and 21 assume that the year has 366 days and all birthdays are equally likely. In Exercise 19 assume it is equally likely that a person is born in any given month of the year.