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a. If having a dog and a cat were disjoint events, it would mean that households in the town cannot have both a dog and a cat simultaneously. In this case, the events of owning a dog and owning a cat do not overlap. So, if a household has a dog, it cannot have a cat, and vice versa.
b. On the other hand, if having a dog and a cat were independent events, it would mean that the probability of a household having a dog does not affect the probability of that same household having a cat, and vice versa. In other words, the occurrence of one event (owning a dog) does not impact the likelihood of the other event (owning a cat).
c. Having a dog or a cat can be both independent and disjoint at the same time. This is because independence refers to the probability of one event not affecting the probability of another event, while disjointedness means the events have no overlap. So, in this case, it is possible for households to have either a dog or a cat independently (meaning having one does not impact the likelihood of having the other), and at the same time, the events are disjoint (meaning households cannot have both a dog and a cat simultaneously).
