The following Venn diagram shows two events 𝐴 and 𝐵. Determine 𝐴 minus 𝐵.
In order to answer this question, we will begin by listing the elements in event 𝐴 and event 𝐵. Circle 𝐴 in the Venn diagram contains the integers one, two, three, five, and eight. And we can write these elements using set notation as shown. In the same way, event 𝐵 contains the integers one, three, four, six, and nine. Two of these numbers, one and three, appear in both sets. This means that the intersection of 𝐴 and 𝐵 contains the numbers one and three.
In this question, we are trying to determine 𝐴 minus 𝐵. This is all the elements that are in set 𝐴 but not set 𝐵. 𝐴 minus 𝐵 is therefore the set containing the numbers two, five, and eight. This leads us to the difference rule, which states that 𝐴 minus 𝐵 is equal to 𝐴 minus 𝐴 intersection 𝐵. We can also use this rule to help determine probabilities of events.