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Mathematics-Online lexicon: Annotation to

Relations between logical operations


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The following rules apply to logical operations:

These alternative representations are often used in proofs.

A logical formula, the truth value of which is independent from the truth values of the statements involved, is called a tautology if it is always true, or a contradiction if it is always false. Such a formula may be replaced by t (also symbolized by $ 1$) or f (also symbolized by 0) respectively. In particular the following identities hold:

$\displaystyle A \lor \lnot A = \mathrm{w}$ $\displaystyle \textrm{and}$ $\displaystyle A\land \lnot A = \mathrm{f}\,,$  
$\displaystyle A \lor \mathrm{w} = \mathrm{w}$ $\displaystyle \textrm{and}$ $\displaystyle A\land \mathrm{w} = A\,,$  
$\displaystyle A \lor \mathrm{f} = A$ $\displaystyle \textrm{and}$ $\displaystyle A\land \mathrm{f} =
\mathrm{f}\,.$  


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  automatisch erstellt am 19.  8. 2013