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I was reading this pdf booklet I found on the internet from MIT to teach myself probability, but they use these symbols to represent DeMorgan's laws:

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I know and understand the laws, but not the symbols as used here. I can't seem to figure them out and I don't want to continue reading without knowing them. Could someone please identify them for me?

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  • $\begingroup$ Those are de Morgan's Laws. Google them. $\endgroup$ – DonAntonio Aug 15 '13 at 23:13
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$^C$ represents the complement of a set.
$\bigcup\limits_n$ is the union over all $n$.
$\bigcap\limits_n$ is the intersection over all $n$.

Thus, the first law reads as:
The complement of the union over all $n$ of $S_n$ is equal to the intersection over all $n$ of the complement of $S_n$.

And the second law reads as:
The complement of the intersection over all $n$ of $S_n$ is equal to the union over all $n$ of the complement of $S_n$.

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  • $\begingroup$ where n and Sn means what? $\endgroup$ – FutureSci Aug 15 '13 at 23:16
  • $\begingroup$ If it's unspecified in the text, I don't know what it would mean there, but my guess would be that there is some indexing set $I$ such that for each $n \in I$, there is a set $S_n$. If I isn't specified, my first guess would be that it is the natural numbers, but that's nothing more than a guess. Moreover, I believe that these laws hold regardless of what the indexing set is, so it doesn't matter too much. $\endgroup$ – qaphla Aug 15 '13 at 23:18

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