## 1.1. Notation and Set Theory

### Definition 1.1.1: Sets and Operations on Sets

A

**set**is a collection of objects chosen from some universe. The universe is usually understood from the context. Sets are denoted by capital letters or curly brackets.**A****B**:**A**is a**subset**of**B**means that every element in**A**is also contained in**B**.**A****B**:**A union B**is the set of all elements that are either in**A**or in**B**or in both sets.**A****B**:**A intersection B**is the set of all elements that are in both sets**A**and**B**.**A \ B**: A**minus B**are all elements from**A**that are not in**B**.- comp(
**A**): The**complement**of**A**consists of all elements that are not in**A**. - Two sets are
**disjoint**if**A****B**=**0**(the empty set) - Two sets
**A**and**B**are**equal**if**A****B**and**B****A**