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Homework Help: Please, help me understand how these interval problems are solved

  1. Jun 30, 2011 #1
    1. The problem statement, all variables and given/known data


    1. (-∞, -2) ∩ [-2, ∞)

    2. (-∞, 5] ∩ [5, ∞)

    3. (-∞, 5) U (4, ∞)

    4. (-∞, 5) ∩ (3, ∞)

    2. Relevant equations

    3. The attempt at a solution

    It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these problems should be solved. The text I am using just gives the definition and quickly glosses over since intervals are not the primary aim of it.
    Would someone be so kind as to explain how I should go about solving these problems. Many thanks.
  2. jcsd
  3. Jun 30, 2011 #2


    Staff: Mentor

    The ∩ symbol means "intersect," which means the numbers that belong to both intervals. What numbers are less than -2 AND greater than or equal to -2?

    Another approach is to draw the two intervals on the number line, to see which numbers are in both intervals.
    The U symbol means "union," which means the numbers that are in the first interval OR are in the second interval. A number belongs to the union of two intervals if it is in either or both intervals.
  4. Jul 1, 2011 #3


    User Avatar

    Staff: Mentor

    An open interval has its end point denoted by a round parenthesis: (

    A closed interval has its end point denoted by a square bracket: [

    Forgotten all this? Google is your best lead for on-line resources. Here's a start: http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html
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