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

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- Mar 13th 2013, 01:44 AMbaxy77baxset 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 - Mar 13th 2013, 03:44 AMPlatoRe: set operations
- Mar 13th 2013, 05:32 AMbaxy77baxRe: 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 - Mar 13th 2013, 05:47 AMPlatoRe: set operations
- Mar 21st 2013, 05:19 AMHallsofIvyRe: 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, $\displaystyle x\in \cup E$.