Here if two events have some overlap means they can happen at the same time, shouldnt this be a case of independent only, could anyone tell me an example in which partial overlap is not independant. The answer apparently is false.

Here too shouldnt it be p and q must be independant, as probability is 1.3 and there is some overlap.

The events are independent ONLY if the overlap is equal to P(A) x P(B). They can still overlap without being independent (for example complete dependence).

oh got it thank you