Video: Finding the Union of Two Sets Using Venn Diagrams

Using the Venn diagram, find 𝑋 ∪ 𝑌.

01:09

Video Transcript

Using the Venn diagram, find 𝑋 ∪ 𝑌.

This symbol means union. The union of two sets includes the elements that belong to either or both sets. The elements of set 𝑋 can be found in this oval. Therefore, 𝑋 includes two, four, six, five, and seven. The elements of set 𝑌 can be found in this box, which includes elements five, seven, three, eight, and one.

Where the shapes overlap are the elements that are included in both sets. The rest are just either in 𝑋 or just in 𝑌. So we need to list all of these elements, the ones that are in 𝑋, the ones that are in 𝑌, and the ones that are in both 𝑋 and 𝑌.

Therefore, the union of 𝑋 and 𝑌 is — and the order that we write these does not matter, so we can begin anywhere — two, four, six, five, seven, three, eight, and one. And this will be our final answer.

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