# Question Video: Finding the Union of Two Sets Using Venn Diagrams Mathematics • 10th Grade

Use the Venn diagram to find 𝑋 ∪ 𝑍.

02:04

### Video Transcript

Use the Venn diagram to find the union between sets 𝑋 and 𝑍.

Let’s start by having a good look at this Venn diagram. What does it show us? Well to start with, we can see three sets. And each set is represented by an oval shape. To begin with, we have set 𝑌. This is the blue oval shape, and this contains the numbers five, eight, seven, and three. To the right of this, we have set 𝑋, which is the green oval shape. This contains the numbers seven, three, one, and even six and two are within set 𝑋. But the interesting thing about set 𝑋 is that there’s a set within it, this orange oval shape that we can see that’s labeled to set 𝑍 or really subset 𝑍. Set 𝑍 contains the numbers six and two.

Now, our question mentions set 𝑋 and 𝑍. It doesn’t mention set 𝑌 at all. But in between them, we have this symbol. When we see this symbol in maths, we know that it represents the union between two sets. And what we mean by the union is everything within those sets. So in other words, what is everything within sets 𝑋 and 𝑍? We need to reall our answer as a set itself. So we need to draw braces and write the numbers in our answer with commas in between to show that they’re different elements of this set. So if we have a set that’s a union between set 𝑋 and 𝑍, what do we have? We have the number seven, three, one, six, and two. So we use the Venn diagram to find the union between sets 𝑋 and 𝑍. The answer is a set containing the elements seven, three, one, six, and two.