# Video: Using a Venn Diagram to Find the Intersection of a Set with the Union of Two Other Sets

Use the Venn diagram below to find (𝑋 ∪ 𝑌) ∩ 𝑍.

01:24

### Video Transcript

Use the Venn diagram below to find the intersection of 𝑋 ∪ 𝑌 and 𝑍.

This symbol means union. It means the elements in either or both sets. This symbol means intersection. It is the elements found in both sets. So let’s first take a look at our Venn diagram. The elements of 𝑌 are three, nine, six, and five. The elements of 𝑋 are six, five, one, seven, and four. The elements of 𝑍 are seven and four.

So let’s begin with finding the union of 𝑋 and 𝑌. So we want the elements that are in either 𝑋 or 𝑌 or in both sets. Three is in set 𝑌. Nine is in set 𝑌. Six is in both 𝑋 and 𝑌. Five is in both 𝑋 and 𝑌. One is in 𝑋. Seven is in 𝑋. And four is in 𝑋.

Now we want to take 𝑋 union 𝑌 and intersect it with 𝑍. So we want to take these elements and intersect them with the elements of 𝑍, seven and four. And the intersection are the elements found in both sets. So what number or numbers is found in both of these sets? Seven and four.

So once again our answer is the elements seven and four.