# 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 π΄ and π΅, what is the set of outcomes for the event (π΄ βͺ π΅)β²?

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### Video Transcript

In sample space S, for events π΄ and π΅, what is the set of outcomes for the event π΄ union π΅ prime?

In this question, weβre asked to consider the event π΄ union π΅ prime. But letβs begin by looking at π΄ union π΅. This is equivalent to π΄ or π΅ occurring. It means that we have all the outcomes when π΄ occurs, and we also need to consider all the outcomes when π΅ occurs. So the event of π΄ union π΅ means all the outcomes that are either event π΄ or event π΅.

The question here asks us, however, about π΄ union π΅ prime. When we have this prime after an event, itβs referred to as the complement of an event. Itβs really everything thatβs not that event. So the complement of π΄ union π΅ are the remaining values in the sample space which donβt fall into the category π΄ union π΅. We can therefore give the answer as a set as the set containing one, two, five, seven, 10, 11, 13, and 14.