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Set Operations and Compound Inequalities definitions

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  • Intersection

    Overlap of elements shared by two sets, often visualized in Venn diagrams and used for 'and' compound inequalities.
  • Union

    Collection of all elements from two sets, combining without repetition, associated with 'or' compound inequalities.
  • Venn Diagram

    Visual tool using overlapping circles to illustrate relationships between sets, highlighting intersections and unions.
  • Empty Set

    Set containing no elements, represented by empty brackets or a circle with a slash, important in set operations.
  • Compound Inequality

    Expression linking two inequalities with 'and' or 'or', requiring combined solution sets for accurate representation.
  • Interval Notation

    Method for expressing solution sets using brackets and parentheses to indicate inclusion or exclusion of endpoints.
  • Bracket

    Symbol used in interval notation or graphs to show inclusion of a boundary value in a solution set.
  • Parenthesis

    Symbol in interval notation or graphs indicating exclusion of a boundary value from a solution set.
  • Set Builder Notation

    Format using curly brackets and a 'such that' line to describe solution sets based on variable conditions.
  • Three Part Inequality

    Inequality with a variable expression between two inequality symbols, requiring operations on all three sides.
  • Solution Set

    Collection of values satisfying an inequality or system, often represented graphically or in interval notation.
  • Graph

    Visual representation of solution sets on a number line, using brackets, parentheses, or circles for endpoints.
  • Overlap

    Region where two sets share common elements, central to finding intersections in compound inequalities.
  • Inequality Symbol

    Character such as <, >, ≤, or ≥ used to compare values and define boundaries in solution sets.
  • Element

    Individual value or member within a set, crucial for determining intersections, unions, and solution sets.