Question Video: Describing the Outcomes of the Complement of a Union of Events Represented on a Venn Diagram Mathematics

In sample space S, for events 𝐴 and 𝐵, what is the set of outcomes for the event (𝐴 ∪ 𝐵)′?

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Video Transcript

In sample space S, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 union 𝐵 prime?

In this question, we’re asked to consider the event 𝐴 union 𝐵 prime. But let’s begin by looking at 𝐴 union 𝐵. This is equivalent to 𝐴 or 𝐵 occurring. It means that we have all the outcomes when 𝐴 occurs, and we also need to consider all the outcomes when 𝐵 occurs. So the event of 𝐴 union 𝐵 means all the outcomes that are either event 𝐴 or event 𝐵.

The question here asks us, however, about 𝐴 union 𝐵 prime. When we have this prime after an event, it’s referred to as the complement of an event. It’s really everything that’s not that event. So the complement of 𝐴 union 𝐵 are the remaining values in the sample space which don’t fall into the category 𝐴 union 𝐵. We can therefore give the answer as a set as the set containing one, two, five, seven, 10, 11, 13, and 14.