Re: Logic and Truth Tables with Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg129953] Re: Logic and Truth Tables with Mathematica?*From*: Dana DeLouis <dana01 at icloud.com>*Date*: Wed, 27 Feb 2013 23:44:34 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

> Can Mathematica, given a relation such as P->Q generate the truth table? Hi. You are looking for the function 'BooleanTable If interested, here is a custom function that I use. The 2 heading rows are written in both normal form, and traditional form. You can add any additional intermediate steps. I've added line numbers to the output. If it finds a possible shorter version, it is added to the end of the table. TruthTable[Implies[P,Q]] For another example, I want to add 'And[p,s] to the table. The last column has a suggestion for a shorter version. equ=(((p||q)&&(p\[Implies]r)&&(q\[Implies]s))&&p)||q; TruthTable[equ, {And[p,s]} ] = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 9 = = = = = = = = = = TruthTable[equ_,steps_List:{}]:=Module[{v,data,min,hdg}, (* Note: For steps, add any intermediate steps would like to see inside { } Note: Requiers Aux Function 'BoolMin[ ] *) v = BooleanVariables[equ]; v=Join[v,BooleanVariables[steps]] //Union; AppendTo[v,{steps,equ}]; (* If shorter version found, add that to the end as a possible suggestion *) min=BoolMin[equ]; If[UnsameQ[min,equ],AppendTo[v,min]]; v=Flatten[v]; (* Calculate table *) data=BooleanTable[v]; (* Adjust Table Data *) data = data/.{True->Style["T",Blue,Bold],False->Style["F",LightGray]}; (* Add Ref numbers *) data=Join[Map[List,Range[Length[data]]],data,2]; (* Add 2 Heading Rows *) (* Normal Form, and Traditional Form *) hdg = Join[{"#"},v]; PrependTo[data,Style[TraditionalForm[#],Bold]&/@hdg]; PrependTo[data,hdg]; (* Clear the upper left corner *) data =ReplacePart[data,{1,1}->""]; Grid[data, Frame->All, Alignment->Center, ItemSize->Automatic, Background -> = {None,{LightBlue,LightBlue},{{{3,-1},{-1,-1}}->LightYellow}} ] ] = = = = = Aux Function = = = = = // Attempts to find a shorter version by trying all options. BoolMin[equ_]:=Module[{opts,v,len}, opts = {"DNF","SOP","CNF","POS","ANF","NOR","NAND","AND","OR"} ; v=BooleanMinimize[equ,#]&/@opts; (* Place Original equation at beginning of list *) PrependTo[v,equ]; len=LeafCount/@v; (* With multiple Minimum leaf counts, if original equation is in list, then keep that *) First[Pick[v,len,Min[len]]] ] = = = = = = = = = = On Thursday, July 12, 2001 3:01:44 AM UTC-4, hea... at in-tch.com wrote: > Hi, > Can Mathematica, given a relation such as P->Q generate the truth table? > Is there a book available that talks about Mathematica and logic? > Thanks, > Heath