Probability and Independence

Hi,
I understand that if events are independent that means if and only if P(A | B) = P(A) or, equivalently, P(B | A) = P(B).
but what about the (Addition Rule for Probabilities), if the events are independent what would be the formula for (OR situation)? Is it the same? i mean : P(E or F) = P(E) + P(F) - P(E and F)
if yes WHY? and if no then what is it?

what about dependent events? what would be the conditional and joint formulas?
plz explain.