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

Given π = {0, 2, 5}, π = {9, 5}, and a universal set π = {5, 8, 9, 2, 1, 0}, find the complement of π β© π.

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### Video Transcript

Given π is the set with elements zero, two, and five, and π is a set with elements nine and five, and a universal set π with elements five, eight, nine, two, one, and zero, find the intersection of the complement of π and π.

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 π is the set with elements zero, two, and five. But thatβs not what weβre looking for. Weβre actually using the complement of π. And this will be all of the elements of π the universal set, except those found in the set π.

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 π, we want those elements of π 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? Weβ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.