Given that 𝐴 and 𝐵 are two events in a sample space of a random experiment, where 𝐵 is a subset of 𝐴, determine 𝐵 minus 𝐴.
The notation 𝐵 minus 𝐴 denotes the difference of two events. In general, we say that 𝐵 minus 𝐴 is the set of elements 𝑥 that occur in event 𝐵 and do not occur in event 𝐴. In this question, we are told that 𝐵 is a subset of 𝐴. Let’s consider what this looks like on a Venn diagram. If 𝐵 is a subset of 𝐴 as in this case, then every element of 𝐵 is also in 𝐴. The entire circle representing the elements in event 𝐵 is contained in the circle representing the elements in event 𝐴.
It is clear from the definition and the diagram that there are no elements of event 𝐵 that are not in event 𝐴. This means that if 𝐵 is a subset of 𝐴, then 𝐵 minus 𝐴 is the empty set.