(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 26368, 999]*) (*NotebookOutlinePosition[ 27032, 1022]*) (* CellTagsIndexPosition[ 26988, 1018]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["The Biconditional Problem", "Section"], Cell["\<\ This isn't a really \"pure\" biconditional in so much as I am not \ using (p\[Implies]q)\[Equal](q\[Implies]p), but let's pretend for now.\ \>", \ "Text"], Cell[CellGroupData[{ Cell["Generate some truth tables", "Subsection"], Cell[CellGroupData[{ Cell["Generate a list of truth value pairs", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(tt = 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Cell[TextData[{ "Create an expression that should evaluate to ", StyleBox["True", FontSlant->"Italic"], "." }], "Subsection"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " just stares at it." }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\((\((a \[And] b)\) \[Or] c)\) == \((\((a \[Or] c)\) \[And] \((b \[Or] c)\))\)\)], "Input"], Cell[BoxData[ \(\((\((a && b)\) || c)\) \[Equal] \((\((a || c)\) && \((b || c)\))\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Perhaps ", StyleBox["we", FontSlant->"Italic"], " can do better than that" }], "Subsubsection"], Cell["\<\ We create a function which takes a logical statement and a count \ for the number of variables in the statemnt.\ \>", "Text"], Cell[BoxData[ \(TruthTable[s_, argc_] := Module[\[IndentingNewLine]{tt = Tuples[{True, False}, argc]}, \[IndentingNewLine]\({#, s @@ #} &\) /@ tt // TableForm\[IndentingNewLine]]\)], "Input"], Cell[BoxData[{ \(t1[a_, b_, 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