# Section 2.3: Applications of Sets

## 2.3 Outline

1. Combined operations with sets
1. order of operations
2. Venn diagrams
2. De Morgan’s laws
3. Venn diagrams with three sets
4. Survey problems

## 2.3 Essential Ideas

Combined Operations

For combined operations, perform operations in parenthesis first, then proceed from left to right. To find a complement, first find the set under the overbar, and then shade all parts not contained under the overbar.

De Morgan’s Laws

There are two parts to De Morgan’s Law.
The complement of a union is the intersection of the complements.
The complement of an intersection is the union of the complements.

Survey Problems

Draw intersecting circles to represent the different categories (sets) in the
survey.

Next, try to determine the number of elements in the intersection of all of the
sets.

Fill in the other inner portions.

Work from the inner portions to the outer portions, being sure to subtract the
numbers in the portions already accounted for; move systematically from one region to another.