# Sets

A set is an unordered group of items, called elements. Some important terminology:

• Union: the union of two sets, denoted $\cup$, refers to the elements that are in at least one of the two sets. For example, $\{1,2,3\} \cup \{3,4,5\} = \{1,2,3,4,5\}$.

• Intersection: the intersection of two sets, denoted $\cap$, refers to the elements that are in both sets. For example, $\{1,2,3\} \cap \{3,4,5\} = \{3\}$.

• Complement (Absolute): Denoted $^c$, the absolute complement refers to all the elements that are not in a set. Considering only the integers, $\{ 1, 2, 3 \}^c$ would represent all integers except 1, 2, or 3.

• Complement (Relative): The relative complement, denoted $\backslash$, refers to elements that are in the first set but not the second. For example: $\{1,2,3\} \backslash \{3,4,5\} = \{1,2\}$

• Symmetric Difference: The symmetric difference, denoted $\triangle$, refers to elements which are in at least one of the sets but not both. For example, $\{1,2,3\} \triangle \{3,4,5\} = \{1,2,4,5\}$.

Note by Arron Kau
5 years, 5 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$