Use the Venn diagram below to find 𝐵 ∪ 𝐶.
This symbol in the question represents the idea of a union between two sets. And here we’re talking about the union between set 𝐵, which is represented here by the orange oval in the Venn diagram, and also set 𝐶, which is the blue circle in our Venn diagram. The union between two sets means we need to include all the elements in both and in either set. In other words, if we put both sets together, we make a union between both sets. What elements do we have?
The elements of set 𝐵 are all the numbers that are in the orange oval. So the elements are two, four, eight, nine, and one. The elements of set 𝐶 are all the numbers that are in the blue circle. So that’s nine, one, three, and six. Notice that two of our numbers appear in both sets.
Of course, in our Venn diagram, this is the part where our oval and our circle overlap. We can see the nine and the one in there. But the union between 𝐵 and 𝐶 must contain all the elements in both sets, which is nine and one, and in either set. In other words, all of the elements. And so 𝐵 ∪ 𝐶 equals two, eight, four, nine, one, six, and three. This is the set we get when we combine sets 𝐵 and 𝐶 together.