Given:
- P(B) = 0.3
- P(A but not B) = 0.4
- P(not A) = 0.6

To determine the relationship between events A and B, we need to consider their intersection and union probabilities.

Intersection Probability:
- P(A and B) = P(A) + P(B) - P(A or B) (by the addition rule of probability)
- P(A or B) = P(A) + P(B) - P(A and B) (by the subtraction rule of probability)

Since we don't have information about P(A) or P(A or B), let's use the given probabilities to find P(A and B) and see if it helps us identify the relationship between A and B.

P(A and B) = P(B) - P(A but not B) (by the definition of conditional probability)
P(A and B) = 0.3 - 0.4
P(A and B) = -0.1

Uh-oh, we have a problem! A probability cannot be negative, so there must be an error in the given probabilities. Let's assume that the correct probability for P(A but not B) is 0.2 instead of 0.4 (which would make more sense given the other probabilities).

P(A and B) = P(B) - P(A but not B) (by the definition of conditional probability)
P(A and B) = 0.3 - 0.2
P(A and B) = 0.1

Great, now we have a valid probability for the intersection of A and B. Let's use it to determine the relationship between A and B.

Mutually Exclusive Events:
- If P(A and B) = 0, then events A and B are mutually exclusive (i.e., they cannot occur at the same time).

Since P(A and B) = 0.1, events A and B are not mutually exclusive. Therefore, option D (mutually exclusive) is not the correct answer.

Independent Events:
- If P(A and B) = P(A) * P(B), then events A and B are independent (i.e., the occurrence of one event does not affect the probability of the other event).

Let's see if events A and B are independent.

P(A and B) = P(A) * P(B) (if events A and B are independent)
0.1 = P(A) * 0.3
P(A) = 0.1 / 0.3
P(A) = 1/3

P(B and not A) = P(B) - P(A and B) (by the definition of conditional probability)
P(B and not A) = 0.3 - 0.1
P(B and not A) = 0.2

P(B and not A) = P(B) * P(not A) (if events A and B are independent)
0.2 = 0.3 * 0.6

Uh-oh, we have another problem! If events A and B were independent, then the product rule of probability would hold for all possible combinations of A and B. However, we found a combination where the product rule does not hold (i.e., P(B and not A) ≠ P(B) * P(not A)).