Question Video: Using Venn Diagrams to Perform Operations Involving Intersection and Complementary Sets | Nagwa Question Video: Using Venn Diagrams to Perform Operations Involving Intersection and Complementary Sets | Nagwa

# Question Video: Using Venn Diagrams to Perform Operations Involving Intersection and Complementary Sets

Use the Venn diagram below to find (π bar β© π bar) β© π bar.

02:42

### Video Transcript

Use the Venn diagram below to find the intersection of π bar with the intersection of π bar and π bar.

Letβs begin by recalling what we mean by the notation in the question. The n symbol means the intersection or βand.β For the part of our question in the parentheses or brackets, we need to find the set of numbers that are in π bar and in π bar. The notation π bar, sometimes written as π prime, means the complement of π. This is the set of all values that are not in π.

We can see from the Venn diagram that the three values zero, three, and six lie in set π. This means that π bar or the complement of π contains all the other values in the Venn diagram: one, two, four, five, seven, and nine. Note that the number eight does not appear inside this Venn diagram. The set of values contained within π are zero, one, four, and five. This means that π bar, or the complement of π, contains two, three, six, seven, and nine.

The set of values in the intersection of π bar and π bar will be contained in both of these sets. There are three such numbers: two, seven, and nine. These are the three numbers that are not in set π and also not in set π.

Set π contains the four numbers one, four, six, and seven. This means that the complement of π is equal to zero, two, three, five, and nine. We need to find the numbers that are in this set and also in the set of the intersection of π bar and π bar. The numbers two and nine exist in both of these sets.

The intersection of π bar with the intersection of π bar and π bar is two and nine. These are the two values that did not exist in any of the three sets. Theyβre not in π, π, or π.

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