If $A$ and $B$ are outcomes for the same sample space $S$, must $A^{\prime} \cup B^{\prime}$ be an event of $S$ ?

Name: If $A$ and $B$ are outcomes for the same sample space $S$, must $A^{\prime} \cup B^{\prime}$ be an event of $S$ ?
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Question

Quizplus · Accepted Answer

The complement of an event and the union of events are both operations that result in subsets of the sample space $S$, so $A^{\prime} \cup B^{\prime}$ is also a subset of $S$ and thus an event in $S$.

If AAA And BBB Are Outcomes for the Same Sample Space SSS , Must

If $A$ And $B$ Are Outcomes for the Same Sample Space $S$ , Must