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.