Results 1 to 2 of 2

Math Help - Sets

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    154

    Sets

    If  A \subseteq B , show that  P(A) \leq P(B) .

    So  B = A \cup (A' \cap B)

    And  P(A \cup B) = P(B) ,  P(A \cap B) = P(A) , and  P(A) = P(B) - P(A' \cap B)  = P(A \cup B) - P(A' \cap B) .

    Does this imply that  P(A) \leq P(B) ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    0 \le P\left( {A' \cap B} \right)\; \Rightarrow \;P(A) \le P(A) + P\left( {A' \cap B} \right) = P(B)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Open sets and sets of interior points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 9th 2011, 03:10 AM
  2. Metric spaces, open sets, and closed sets
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 16th 2011, 05:17 PM
  3. Replies: 9
    Last Post: November 6th 2010, 12:47 PM
  4. Approximation of borel sets from the top with closed sets.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 18th 2010, 08:51 AM
  5. how to show these sets are 95% confidence sets
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 11th 2009, 09:08 PM

Search Tags


/mathhelpforum @mathhelpforum