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In sample space S, for events π΄ and π΅, what is the set of outcomes for the event π΄ union π΅ prime?
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In this question, weβre asked to consider the event π΄ union π΅ prime.
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But letβs begin by looking at π΄ union π΅.
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This is equivalent to π΄ or π΅ occurring.
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It means that we have all the outcomes when π΄ occurs, and we also need to consider all the outcomes when π΅ occurs.
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So the event of π΄ union π΅ means all the outcomes that are either event π΄ or event π΅.
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The question here asks us, however, about π΄ union π΅ prime.
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When we have this prime after an event, itβs referred to as the complement of an event.
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Itβs really everything thatβs not that event.
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So the complement of π΄ union π΅ are the remaining values in the sample space which donβt fall into the category π΄ union π΅.
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We can therefore give the answer as a set as the set containing one, two, five, seven, 10, 11, 13, and 14.