# 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
4 years, 1 month ago

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