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Is there a technical difference between boolean formulas and boolean functions?

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A Boolean formula is a concrete string of symbols. A Boolean function of $n$ inputs is an assignment of output truth values to each possible choice of $n$ input truth values.

For example, "$p\lor q$" and "$q\lor (p\land\neg q) $" are two different formulas. They happen to describe the same Boolean function of two variables.

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    $\begingroup$ You're too fast. $\endgroup$ – dfeuer Dec 8 '13 at 5:41
  • $\begingroup$ @dfeuer: Sorry? $\endgroup$ – Henning Makholm Dec 8 '13 at 5:43
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    $\begingroup$ Just don't do it again :-P. $\endgroup$ – dfeuer Dec 8 '13 at 5:44
  • $\begingroup$ Also formula is part of language's syntax while Boolean function is part of interpretation (semantics). $\endgroup$ – Trismegistos Dec 9 '13 at 12:58

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