Question Video: Finding the Union of the Complements of Two Sets Using a Given Venn Diagram | Nagwa Question Video: Finding the Union of the Complements of Two Sets Using a Given Venn Diagram | Nagwa

# Question Video: Finding the Union of the Complements of Two Sets Using a Given Venn Diagram

Using the Venn diagram, find π bar βͺ π bar.

02:17

### Video Transcript

Using the Venn diagram, find the union of π bar and π bar.

Letβs begin by defining some of the notation in this question. The U or union symbol means βor.β This means weβre looking for the set of values that are in π bar or in π bar. π bar means the complement of π. This is all the values that are not in set π. Likewise, π bar or the complement of π is the set of values not in π. We need to find the set of values that are not in π or not in π.

We can see from the Venn diagram that π contains the set of values three, six, seven, and nine. The complement of π or those values not in π will be all the other values, in this case, one, two, four, five, and eight. The numbers in set π are one, three, five, and nine. The numbers not in set π or the complement of π are two, four, six, seven, and eight. We need to select all the numbers that are either not in π or not in π.

Two, four, and eight appear in both of these lists. But we do not need to write them twice. The set of numbers that appear in the complement of π or the complement of π are one, two, four, five, six, seven, and eight. This is actually all of the numbers except three and nine. These are the numbers that appear in both π and π. We can therefore conclude that the union of the complement of π and the complement of π is everything apart from the intersection of π and π.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions