Truth Table for n Variables.html

Truth Table for n Variables

> restart:

> iff:=proc(p,q)
(p implies q) and (q implies p);
end proc:

Enter the number of logically independent propositional variables after n:=

> n:=3;

Enter the compound proposition to be analyzed after f: For connectives use: not, and, or, implies. For variables use p1, p2, . . . , pn. You may also use iff as a connective by writing p iff q as iff(p,q).

> f:=((p1 implies p2) and (p2 implies p3) and (p3 implies p1)) implies ((p1 implies p3) and (p2 implies p3) and (p3 implies p1));

> ;

> TT:=Array(1..1+2^n,1..1+n): #Create an array of the appropriate dimensions for the truth-table.

> for j from 1 to n do #Title the truth-table.
TT[1,j]:=cat("p",convert(j,string))
end do:

> prop:=convert(f,string):

> if length(prop)>115
then TT[1,n+1]:="f"
else TT[1,n+1]:=prop
end if:

> for j from 1 to n do     #For all the independent variable entries in the array enter false.
    for i from 2 to 2^n+1 do
           TT[i,j]:=false
    end do
end do:

> for j from 1 to n do     #In each column enter the initial block of T's.
    for i from 2 to 2^n+1 do
          if i-1<=2^(n-j) then TT[i,j]:=true
    end if
    end do
end do:

> for j from 1 to n do   #Extend the initial block of T's & F's to the rest of the column.
    for i from 2+2^(n-j+1) to 1+2^n do
            for k from 2 to 1+2^(n-j) do
                  if i mod 2^(n-j+1) = k mod 2^(n-j+1) then TT[i,j]:=TT[k,j]
                  end if
            end do
    end do
end do:

> for i from 2 to 1+2^n do     #On each row evaluate the independent variables, then evaluate f
    for j from 1 to n do
         p||j:=TT[i,j]
    end do:
    TT[i,n+1]:=evalb(f)
end do:

> if length(prop)>115 then print("f = "||prop) end if; TT;

If n>3, then a small rectangle appears in lieu of the truth-table. Left-click on this rectangle to view the truth-table as a spread-sheet.

> f:='f':