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Math Help - set operations

  1. #1
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    set operations

    hi,

    can anyone show me why is this true:

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

    P is a probability function

    thank you
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  2. #2
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    Re: set operations

    Quote Originally Posted by baxy77bax View Post
    can anyone show me why is this true:
    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 A~\&~B are events and A\subseteq B then \mathcal{P}(A)\le\mathcal{P}(B).

    Simply apply that here.
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  3. #3
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    Re: set operations

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

    \cap E  \subset \cup E

    or is this an axiom
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  4. #4
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    Re: set operations

    Quote Originally Posted by baxy77bax View Post
    ok i get it , however i still don't get how to show that
    \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 A\cap B\subseteq A\cup B~?
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  5. #5
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    Re: set operations

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

    If x\in \cap E, then x is in every set in E. So certainly, x\in \cup E.
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