Write the set 𝑋 using the listing method.
In order to use the listing method, we need to write all of the elements of 𝑋 horizontally, meaning left to right. So let’s look at our Venn diagram first. All of the elements of 𝑋 will be found in this oval. And all of the elements of 𝑌 will be found in this oval. So how can they overlap?
This little part represents the intersection of sets 𝑋 and 𝑌, meaning the elements that they have in common. So set 𝑋 has element eight and five. But, so does 𝑌. So we want to write the set 𝑋, so all of the elements that are in 𝑋. So 𝑋 will include elements six — and now I’ll write the next one right next to it, to the right of it — three. And the order at which we write these does not matter, nine, eight, and five. And we put braces on each side to show that these are all of the elements that are in 𝑋.
So using the listing method, we wrote the elements horizontally left to right. And the elements were six, three, nine, eight, and five.