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Set Operations and Compound Inequalities definitions

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  • Intersection
    Values shared by two sets, visually represented as the overlap in a Venn diagram, crucial for 'and' compound inequalities.
  • Union
    All values from either set combined, with no repetition, associated with 'or' compound inequalities.
  • Set
    A collection of distinct elements, often represented with curly brackets or in a Venn diagram.
  • Venn Diagram
    Overlapping circles used to visually display relationships between sets, highlighting intersection and union.
  • Empty Set
    A set containing no elements, denoted by empty brackets or a circle with a slash.
  • Compound Inequality
    Two inequalities linked by 'and' or 'or', requiring combined solution sets.
  • Interval Notation
    A concise way to express solution sets using brackets and parentheses to indicate inclusion or exclusion.
  • Bracket
    Symbol used in interval notation to show a value is included in the solution set.
  • Parenthesis
    Symbol in interval notation indicating a value is excluded from the solution set.
  • Solution Set
    All values satisfying an inequality or equation, often graphed or written in interval notation.
  • Element
    An individual value or member within a set, such as a number in a list.
  • Standard Form
    A conventional way to write mathematical expressions, aiding clarity in advanced algebra.
  • Symbol
    A character representing mathematical concepts, such as ∩ for intersection or ∪ for union.
  • Graph
    A visual representation of solution sets, often used to illustrate inequalities and their relationships.
  • Overlap
    The shared region between sets, central to finding intersections in compound inequalities.