Video: Finding the Complement of the Union of Two Sets Using Venn Diagrams

Using the Venn diagram, find not (𝑋 βˆͺ π‘Œ)

01:42

Video Transcript

Using the Venn diagram, find not 𝑋 union π‘Œ.

It’s worth noting that other notation can be used for this kind of question, like this. So we got 𝑋 union π‘Œ inside of the parentheses. And we’ve got a prime, which also denotes that it means not 𝑋 union π‘Œ. But what does not 𝑋 union π‘Œ mean. Well, we can think about it as not 𝑋 or π‘Œ, and that’s because union means or.

So how would this look on a Venn diagram? Well, if I was to draw a sketch of a Venn diagram, which we have here. We’ve got 𝑋 and π‘Œ. Well, if we would say everything in 𝑋, it would look like this. But we want 𝑋 or π‘Œ. So what I’ve done now is shade in π‘Œ. So that means 𝑋 or π‘Œ would be anything in 𝑋 or anything in π‘Œ. It’s not and so it doesn’t have to be both. It means anything there at all.

So therefore, if we’re looking for not 𝑋 or π‘Œ or not 𝑋 union π‘Œ, then therefore, it’s gonna be anything that is not shaded in pink. So what I’ve done is I’ve shaded in blue. So it’s all the area around the outside. So therefore, in our question, all the area around the outside contains the three numbers three, seven, and nine. So therefore, we can say that the set of numbers that satisfy not 𝑋 union π‘Œ are going to be nine, three, and seven.

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