Question Video: Determining the Difference of Two Events Mathematics

Given that 𝐴 and 𝐡 are two events in a sample space of a random experiment, where 𝐡 βŠ‚ 𝐴, determine 𝐡 βˆ’ 𝐴.

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Video Transcript

Given that 𝐴 and 𝐡 are two events in a sample space of a random experiment, where 𝐡 is a subset of 𝐴, determine 𝐡 minus 𝐴.

The notation 𝐡 minus 𝐴 denotes the difference of two events. In general, we say that 𝐡 minus 𝐴 is the set of elements π‘₯ that occur in event 𝐡 and do not occur in event 𝐴. In this question, we are told that 𝐡 is a subset of 𝐴. Let’s consider what this looks like on a Venn diagram. If 𝐡 is a subset of 𝐴 as in this case, then every element of 𝐡 is also in 𝐴. The entire circle representing the elements in event 𝐡 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 𝐡 that are not in event 𝐴. This means that if 𝐡 is a subset of 𝐴, then 𝐡 minus 𝐴 is the empty set.

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