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}∪{3,4,5}={1,2,3,4,5} \{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}∩{3,4,5}={3} \{1,2,3\} \cap \{3,4,5\} = \{3\}.

  • Complement (Absolute): Denoted c ^c, the absolute complement refers to all the elements that are not in a set. Considering only the integers, {1,2,3}c \{ 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}\{3,4,5}={1,2} \{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}△{3,4,5}={1,2,4,5} \{1,2,3\} \triangle \{3,4,5\} = \{1,2,4,5\}.

Note by Arron Kau
6 years, 9 months ago

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  Easy Math Editor

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\frac{2}{3} 23 \frac{2}{3}
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