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Intermediate Algebra: Inequalities and Sets

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이 집합의 용어 (19)

  • What symbols characterize inequalities?
    Inequalities are characterized by less than, greater than, less than or equal to, and greater than or equal to.
  • What type of brackets are used for strict inequalities?
    Parentheses ( ) are used for strict inequalities: less than < or greater than >.
  • What type of brackets are used for inclusive inequalities?
    Brackets [ ] are used for inclusive inequalities: less than or equal to ≤ and greater than or equal to ≥.
  • What type of brackets are always used with infinity in interval notation?
    Infinity always uses parentheses ( ) in interval notation.
  • What does the interval notation (] represent?
    The interval (] is a half-open interval, meaning one endpoint is excluded (parenthesis) and the other is included (bracket).
  • What does the interval () represent?
    The interval () is an open interval, meaning both endpoints are excluded (parentheses).
  • What does the interval [] represent?
    The interval [] is a closed interval, meaning both endpoints are included (brackets).
  • How is the intersection of two sets represented?
    The intersection of sets A and B is represented by the upside down U symbol: A ∩ B, meaning elements common to both sets.
  • What is set builder notation?
    Set builder notation describes a set as {x | x (inequality) y}, meaning the set of all x such that x satisfies the inequality.
  • What does the vertical bar | mean in set builder notation?
    The vertical bar | means 'such that' in set builder notation.
  • What is a compound inequality?
    A compound inequality is formed by joining two inequalities with 'and' or 'or'.
  • What is a conjunction in inequalities?
    A conjunction is a compound inequality joined by 'and', meaning both conditions must be true.
  • How do parentheses and brackets affect interval endpoints?
    Parentheses ( ) exclude endpoints; brackets [ ] include endpoints in intervals.
  • How is the solution set of an inequality expressed using interval notation?
    The solution set uses parentheses or brackets to show whether endpoints are included or excluded, e.g., (a, b) or [a, b].
  • What does the intersection of sets represent in terms of solutions?
    The intersection represents values that satisfy both sets' conditions simultaneously.
  • How do you write the set of all x greater than 3 in set builder notation?
    It is written as {x | x > 3}.
  • How do you write the interval of all x between 2 and 5, including 2 but excluding 5?
    It is written as [2, 5).
  • What does a compound inequality joined by 'or' mean?
    It means the solution satisfies at least one of the inequalities.
  • Why is infinity always paired with parentheses in interval notation?
    Because infinity is not a number and cannot be included, so it always uses parentheses.