# 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
6 years, 11 months ago

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