# Video: Finding the Set of Outcomes Using a Venn Diagram

In the sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 ⋃ 𝐵?

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### Video Transcript

In the sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴 union 𝐵?

The U notation in this question means union or all. We are looking for those values that are in event 𝐴 or event 𝐵. In event 𝐴, we have the set of numbers three, six, nine, 12, and 15. These are the multiples of three between one and 15 inclusive. In event 𝐵, we have the numbers four, eight, and 12. These are the multiples of four between one and 15. We notice that the number 12 occurs in both of these sets; it is a multiple three and a multiple of four. When writing down the set of outcomes for the event 𝐴 union 𝐵 we only need to write 12 once.

The correct answer is the set of numbers three, four, six, eight, nine, 12, and 15. This is a list of multiples of three or four between one and 15 inclusive. We notice that the numbers outside of the circles one, two, five, seven, 10, 11, 13, and 14 are neither multiples of three nor multiples of four.