### Chapter 3. Probability: Randomness

### Sets, Subsets and Elements

Before introducing the concept of *randomness*, it is important to define the terms *set, element, *and *subset*.

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Sets and Elements

**Definition**

A **set** is a collection of distinct objects, considered as an object in its own right. An object can be anything from a number, a letter, a set or a combination of these.

The distinct objects in a set are called the **elements** of that set.

**Notation**

\[\text{set}=\{\text{element}, \text{element}, \ldots\}\]

For example, the numbers #2#, #4# and #6# are distinct objects when considered separately. But when they are considered collectively, they form a single set with three elements, written as #\{2,4,6\}#.

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Sets of elements are often depicted with the use of a *Venn Diagram*. Sets are usually given a name (e.g. #A#) and are depicted as a circle. The elements of the set (e.g. #1, 2, 3, 4, 5, 6#*)* are then put within the circle. The Venn Diagram below corresponds to the set #A = \{1, 2, 3, 4, 5, 6\}#.

The set #B# is a **subset** of #A# if #B# is *contained* inside of #A#. That is, all elements of #B# are also elements of #A#.

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Subsets are displayed in a Venn diagram as a circle within a circle. The image below shows the set #A = \{1, 2, 3, 4, 5, 6\}# and its subset #B = \{1, 3, 5, 6\}#.

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