Video: Finding the Complement of a Set Using Venn Diagrams

Using the Venn diagram, find the complement of 𝑋.

01:35

Video Transcript

Using the Venn diagram, find the complement of 𝑋.

So it’s the line that’s written on top of 𝑋 that lets us know that this is the complement of 𝑋. And 𝑋 is a set that has elements in it. So we wanna know all of the elements that are not in the set 𝑋. Complement really means at the opposite of it. So here we have the set 𝑋. And the elements in 𝑋 are seven, three, and nine. 𝑒 represents the universal set.

The universal set is like the largest set. It holds all of the elements. So any other set would have to be a subset of that. So 𝑋 here is a subset of the universal set. So here is the symbol for subset. And 𝑋 is a subset of the universal set. Because a subset means all of the elements are also found in another set.

So here, 𝑋 is inside of the universal set. It’s inside of that box. So this means the universal set will include all of the elements from 𝑋, so seven, three, and nine. But it also includes one, eight, and six. So which elements are in the universal set of the whole thing, but the elements that are not in the set 𝑋?

Those would have to be elements one, eight, and six. And the order in which we would write these elements does not matter. So one, eight, and six would be in the compliment of 𝑋.

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