Question Video: Finding the Complement of a Set given the Universal Set

Video Transcript

If the universal set 𝑈 is the set that includes elements six, 10, seven, zero, and three and 𝑋 is the set with elements zero and three, what is the complement of 𝑋?

So first, we’re told that we have a universal set. And the universal set includes all of the elements. And it includes all of the subsets including itself. And it has elements six, 10, seven, zero, and three. So let’s start to draw a Venn diagram.

We know that 𝑈 is the universal set. So it should include all elements. So this should be the biggest thing that we have. And before we begin writing them, let’s look at this subsets, the smaller sets. We have a set 𝑋 and it includes zero and three. And zero and three will also be found in the universal set because it includes all of the elements. So we need to put it inside of the box.

So now that we’ve done that, we need to write the rest of the elements of 𝑈 inside of the box, six, 10, and seven. So we want to know what is the complement of 𝑋. And a complement of a set includes all elements that are not in the set. So which elements are actually not in 𝑋?

Well, we can see 𝑋 hold the elements zero and three. So the only ones that are not in that would be elements six, 10, and seven. And the order that we write these elements does not matter. So this will be our final answer.