Question Video: Finding the Complement of the Union of Three Sets Using a Given Venn Diagram | Nagwa Question Video: Finding the Complement of the Union of Three Sets Using a Given Venn Diagram | Nagwa

# Question Video: Finding the Complement of the Union of Three Sets Using a Given Venn Diagram

Use the given Venn diagram to find the complement of (π βͺ π βͺ π).

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### Video Transcript

Use the given Venn diagram to find the complement of π union π union π.

Well, in this question, the first thing we wanna take a look at is the notation and what it means. Well, we can see that weβve got π union π union π. So we have this U, and what this U means is, as Iβve said, union. But what this can also mean is or. So we could think of it as π or π. So, for instance, in our example, weβd have π or π or π. Then the other bit of notation weβve got is here a bar. And this bar is on top. So in our example, weβve got the bar above the π union π union π. But what does this mean? Well, if weβve got π bar and this means the complements of π, so this means not π. So weβre gonna be looking for the set of values that are not in the set π.

So therefore, for this question, we could think of the complement of π union π union π as the set of values that are not in π or π or π. So, first of all, if weβd look at the set of values that are in π union π union π, then these would be zero, one, two, three, five, seven, nine, 10, 11. And Iβve circled them in pink here. So therefore, if you want to find the complement of π union π union π, so, as weβve said, the set of values not in π or π or π, then this is gonna be the set eight, six.

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