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I know that $X \iff Y$ is true when

  1. $X$ is True and $Y$ is True

  2. $X$ is False and $Y$ is False

I know that there is a simple algorithm to convert to CNF form, but I don't remember it...

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How about $(X \land Y) \lor (\lnot X \land \lnot Y) = (\lnot X \lor Y) \land (X \lor \lnot Y)$ –  Sasha Jan 14 '12 at 18:38

2 Answers 2

up vote 5 down vote accepted

$$(x \leftrightarrow y) \Leftrightarrow (x \rightarrow y) \land (y \rightarrow x) \Leftrightarrow (\lnot x \lor y) \land (\lnot y \lor x) $$

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There is a distinction between $\rightarrow$ and $\Rightarrow$, the former is a connective between propositions within the language, while the latter is in the meta-language. This also made your post somewhat easier to read :-) –  Asaf Karagila Jan 14 '12 at 19:47
    
@AsafKaragila,תודה –  pedja Jan 14 '12 at 19:58

$(\neg X \vee Y)\wedge(X\vee\neg Y)$

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