# Question Video: Describing the Outcomes of the Intersection of Events Represented on a Venn Diagram Mathematics

In the sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 not 𝐵?

01:47

### Video Transcript

In the sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 and not 𝐵?

The notation 𝐵 bar means not 𝐵. This is also sometimes written as 𝐵 prime. The 𝑛 symbol means the intersection. This means we’re looking for outcomes that occur in event 𝐴 and not in event 𝐵. We can see from our Venn diagram that set 𝐴 contains the numbers three, six, nine, 12, and 15. These are the multiples of three between one and 15. Set 𝐵 contains the numbers four, eight, and 12. These are the multiples of four between one and 15. Only one of these values, the number 12, occurs in both set 𝐴 and set 𝐵.

This is the number in the intersection of the two circles. 12 is a multiple of three and a multiple of four. We can therefore conclude that the outcomes for the event 𝐴 and not 𝐵 are three, six, nine, and 15. These are the numbers that are multiples of three and not multiples of four. The set of outcomes for event 𝐴 and not 𝐵 will be equal to the set of outcomes for event 𝐴 minus the set of outcomes for event 𝐴 and 𝐵. These are the outcomes that only occur in set 𝐴.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.