Suppose 𝐴 and 𝐵 are events such that 𝐵 is a subset of 𝐴. Determine 𝐴 union 𝐵.
We will begin by recalling what the set notation in this question means. If 𝐵 is a subset of 𝐴, we know that every element of 𝐵 is in 𝐴 and 𝐴 has more elements. The union of events 𝐴 and 𝐵 contains every element in 𝐴 or 𝐵 or in both 𝐴 and 𝐵. We can represent this information on a Venn diagram as shown, where the circle representing event 𝐵 is entirely contained within the circle representing event 𝐴. As already stated, the union of events 𝐴 and 𝐵 will be anything inside circle 𝐴 or in circle 𝐵 or in both. In this question, since 𝐵 is a subset of 𝐴, then 𝐴 union 𝐵 is simply equal to 𝐴.