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I have a logic expression: f0[a0_, a1_, a2_, a3_] := a0 And Not a1 And Not a2 And a3 Or Not a0 And a2 And a3 Or Not a0 And a1 And a3, I know I should use BooleanTable, but it cannot generate a table like below.

How to generate a truth table in mathematica like below?

enter image description here

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    $\begingroup$ There is the BooleanTable command. Does it help? For creating the corresponding function you can use logical and: && and logical or: || in case you don't know. $\endgroup$ – user59583 Dec 3 '18 at 6:17
  • $\begingroup$ @Buddha_the_Scientist Thank you, I have correct my expression, Of course BooleanTable can help me, but it cannot generate a table like the picture above, it only returns a series of true or false. $\endgroup$ – 余星佑 Dec 3 '18 at 6:23
  • $\begingroup$ Then use the TableForm with the option TableHeadings for the result. Something like: TableForm[{{a, b, c, d}}, TableHeadings -> {None, {"a0", "a1", "a2", "a3"}}] $\endgroup$ – user59583 Dec 3 '18 at 6:24
  • $\begingroup$ @Buddha_the_Scientist, thank you, but how to use my function to generate all series of possible outputs like this? I know that how to generate one possible output commad: TableForm[{{True, False, True, False, f0[True, False, True, False]}}, TableHeadings -> {None, {"a0", "a1", "a2", "a3", "b0"}}] $\endgroup$ – 余星佑 Dec 3 '18 at 6:44
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f = a0 && ! a1 && ! a2 && a3

TableForm[BooleanTable[{a0, a1, a2, a3, f}, {a0, a1, a2, a3}], TableHeadings -> {None, {a0, a1, a2, a3, f}}]

Apparently there are resources like this one or this one

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  • $\begingroup$ Thank you very much! This absolutely solve my quesiton! $\endgroup$ – 余星佑 Dec 3 '18 at 7:20
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truthTableFormattor[rawData_] := Insert[Insert[
Grid[rawData /. {0 -> 0, 
   1 -> Item[1, Background -> Lighter[Magenta]]}, 
 FrameStyle -> Gray, 
 Frame -> All], {Background -> {None, {GrayLevel[0.7], {White}}}, 
 Dividers -> {Black, {2 -> Black}}, Frame -> True, 
 Spacings -> {2, {2, {0.7}, 2}}}, 2], {Dividers -> All, 
Spacings -> .7 {1, 1}}, 2];


truthTable[f__] :=  Module[{}, atoms = Cases[Most[{f}],
 (a_ /;Length[a] == 0 \[And] Not[StringQ[a]])];heads = 
 ToString[TraditionalForm@#] & /@ {f};
  rawData = Transpose@Boole[BooleanTable[#, atoms] & /@ {f}];
  If[Last[{f}] === 1, 
   Transpose@Boole[BooleanTable[#, atoms] & /@ Most[{f}]], 
    If[Last[{f}] === "rev", 
    truthTableFormattor[{ToString[
       TraditionalForm@#] & /@ (Most@{f})}~Join~
      Transpose[(Reverse /@ 
      Boole[BooleanTable[#, atoms] & /@ (Most@{f})])]], 
     truthTableFormattor[{heads}~Join~rawData]]]];




f0[a0_, a1_, a2_, a3_] := a0 \[And] \[Not] a1 \[And] \[Not] a2 \[And] a3;

truthTable[a0, a1, a2, a3, f0[a0, a1, a2, a3]]

enter image description here

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  • $\begingroup$ Wow your answer is more perfect $\endgroup$ – 余星佑 Dec 20 '18 at 2:33

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