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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
3 years, 1 month ago

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