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Question Video: Determining the Difference of Two Events Mathematics

The following Venn diagram shows two events, 𝐴 and 𝐡. Determine (𝐴 βˆ’ 𝐡).


Video Transcript

The following Venn diagram shows two events 𝐴 and 𝐡. Determine 𝐴 minus 𝐡.

In order to answer this question, we will begin by listing the elements in event 𝐴 and event 𝐡. 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 𝐡 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 𝐡 contains the numbers one and three.

In this question, we are trying to determine 𝐴 minus 𝐡. This is all the elements that are in set 𝐴 but not set 𝐡. 𝐴 minus 𝐡 is therefore the set containing the numbers two, five, and eight. This leads us to the difference rule, which states that 𝐴 minus 𝐡 is equal to 𝐴 minus 𝐴 intersection 𝐡. We can also use this rule to help determine probabilities of events.

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