Video: Finding the Intersection of a Set and the Complement of the Other Set

Given 𝑋 = {0, 2, 5}, π‘Œ = {9, 5}, and a universal set π‘ˆ = {5, 8, 9, 2, 1, 0}, find the complement of 𝑋 ∩ π‘Œ.

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Video Transcript

Given 𝑋 is the set with elements zero, two, and five, and π‘Œ is a set with elements nine and five, and a universal set π‘ˆ with elements five, eight, nine, two, one, and zero, find the intersection of the complement of 𝑋 and π‘Œ.

This upside-down U is the intersection. And the intersection of two sets includes all of the elements that are found in both of the sets. So we know that 𝑋 is the set with elements zero, two, and five. But that’s not what we’re looking for. We’re actually using the complement of 𝑋. And this will be all of the elements of π‘ˆ the universal set, except those found in the set 𝑋.

And we know that the universal set includes elements five, eight, nine, two, one, and zero. So to find the elements in a complement of 𝑋, we want those elements of π‘ˆ except for zero, two, and five. So it includes elements eight, nine, and one.

So to find the intersection of these two sets, what elements are found in both? We’ve eight, nine, and one and then nine and five. Well, the only element we found in both is the element nine. Therefore, nine will be our final answer.

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