Results 1 to 5 of 5
Like Tree3Thanks
  • 1 Post By Plato
  • 1 Post By Plato
  • 1 Post By HallsofIvy

Thread: set operations

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    62

    set operations

    hi,

    can anyone show me why is this true:

    $\displaystyle P(\cap_{i=1}^{n}E_{i}) \leq P(\cup_{i=1}^{n}E_{i})$

    P is a probability function

    thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,776
    Thanks
    2823
    Awards
    1

    Re: set operations

    Quote Originally Posted by baxy77bax View Post
    can anyone show me why is this true:
    $\displaystyle P(\cap_{i=1}^{n}E_{i}) \leq P(\cup_{i=1}^{n}E_{i})$
    P is a probability function

    You should have proved that if $\displaystyle A~\&~B$ are events and $\displaystyle A\subseteq B$ then $\displaystyle \mathcal{P}(A)\le\mathcal{P}(B)$.

    Simply apply that here.
    Thanks from baxy77bax
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    62

    Re: set operations

    ok i get it , however i still don't get how to show that

    $\displaystyle \cap E \subset \cup E$

    or is this an axiom
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,776
    Thanks
    2823
    Awards
    1

    Re: set operations

    Quote Originally Posted by baxy77bax View Post
    ok i get it , however i still don't get how to show that
    $\displaystyle \cap E \subset \cup E$ or is this an axiom

    There is no point in your trying to prove any theorem in probability if you are not grounded in set theory.

    Surely you can show that $\displaystyle A\cap B\subseteq A\cup B~?$
    Thanks from baxy77bax
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,771
    Thanks
    3028

    Re: set operations

    Do you understand the definitions of "$\displaystyle \cap$" and "$\displaystyle \cup$"? $\displaystyle x\in A\cap B$ if and only if x is in both A and B. $\displaystyle x\in A\cup B$ if x is in either A or B.

    If $\displaystyle x\in \cap E$, then x is in every set in E. So certainly, $\displaystyle x\in \cup E$.
    Thanks from baxy77bax
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Set Operations
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Nov 6th 2011, 03:55 AM
  2. operations
    Posted in the Algebra Forum
    Replies: 16
    Last Post: Apr 25th 2011, 04:12 PM
  3. Operations 71.4
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Oct 26th 2009, 08:38 AM
  4. Operations - help!
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Nov 16th 2008, 05:35 PM
  5. Replies: 5
    Last Post: Feb 6th 2006, 03:13 AM

Search Tags


/mathhelpforum @mathhelpforum