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6\"h4hI\"pGF%I\"qGF%hF*F)" }{TEXT 211 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 21 "TT:=Array(1..5,1..3):" }{MPLTEXT 1 209 0 "" }}} {EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 18 "T:=true: F:=false:" } {MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 25 " \+ prop:=convert(f,string):" }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> \+ " 0 "" {MPLTEXT 1 209 133 "TT[1,1]:=\"p\": TT[1,2]:=\"q\": TT[1,3]:=pr op: TT[2,1]:=T: TT[2,2]:=T:TT[3,1]:=T:TT[3,2]:=F:TT[4,1]:=F:TT[4,2]:=T :TT[5,1]:=F:TT[5,2]:=F: " }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> \+ " 0 "" {MPLTEXT 1 209 122 " p:=T:q:=T:TT[2,3]:=evalb(f): p:=T:q:=F:T T[3,3]:=evalb(f): p:=F:q:=T:TT[4,3]:=evalb(f): p:=F:q:=F:TT[5,3]:= evalb(f):" }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 3 "TT;" }{MPLTEXT 1 209 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\"'kQ_-I'MATRIXGF%6#7'7%Q\"pF%Q\"qF%QHno t~(p~implies~q)~implies~(q~implies~p)F%7%I%trueGI*protectedGF2F1F17%F1 I&falseGF2F17%F4F1F17%F4F4F1I&ArrayGF2" }{TEXT 211 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 49 "T:='T': F:='F':p:='p':q:='q':f: ='f':prop:='prop':" }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 211 "" 0 "" {TEXT 212 27 "Truth T able for n Variables" }{TEXT 212 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 210 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 9 "restart : " }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 210 75 "Ent er the number of logically independent propositional variables after n :=" }{TEXT 210 0 "" }}{PARA 208 "> " 0 "" {MPLTEXT 1 209 5 "n:=3;" } {MPLTEXT 1 209 0 "" }}{PARA 209 "" 0 "" {TEXT 210 142 "Enter the compo und proposition to be analyzed after f: For connectives use: not, a nd, or, implies. For variables use p1, p2, . . . , pn." }{TEXT 210 0 "" }}{PARA 212 "> " 0 "" {MPLTEXT 1 0 22 "f:= p1 or (p2 and p3);" } {MPLTEXT 1 0 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>I\"nG6\"\"\"$" } {TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"5I#p1GF%3I# p2GF%I#p3GF%" }{TEXT 211 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 96 "TT:=Array( 1..1+2^n,1..1+n): #Create an array of the appropriate dimensions for \+ the truth-table." }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 47 "for j from 1 to n do #Title the truth-table." } {MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 41 "\n TT[1,j]:=cat(\"p\",conv ert(j,string))" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 8 "\nend do:" } {MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 75 "p rop:=convert(f,string): TT[1,n+1]:=prop: length(prop);length(TT[1,n+ 1]);" }{MPLTEXT 1 209 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#\"#:" } {TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#\"#:" }{TEXT 211 0 " " }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 92 "for j from 1 to n d o #For all the independent variable entries in the array enter fal se." }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 30 "\n for i from 2 to 2 ^n+1 do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 27 "\n TT[i,j ]:=false" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 12 "\n end do" } {MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 8 "\nend do:" }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 72 "for j from 1 to n do #In each column enter the initial block of T's." }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 30 "\n for i from 2 to 2^n+1 do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 47 "\n if i-1<=2^(n-j) then TT[i,j] :=true " }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 12 "\n end if" } {MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 12 "\n end do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 18 "\nend do: " }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 88 "for j from 1 to n do #Extend the initial block of T's & F's to the rest of the column." }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 40 "\n for i from 2+2^(n-j+1) to 1+2^n do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 42 "\n \+ for k from 2 to 1+2^(n-j) do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 79 "\n if i mod 2^(n-j+1) = k mod 2^(n-j+1) then TT[i, j]:=TT[k,j]" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 26 "\n \+ end if" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 20 "\n e nd do" }{MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 12 "\n end do" } {MPLTEXT 1 209 0 "" }{MPLTEXT 1 209 17 "\nend do: " }{MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 212 "> " 0 "" {MPLTEXT 1 0 93 "for i from 2 to 1+2^n do #On each row evaluate the independent variables, then evaluate f" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 26 "\n for j from 1 \+ to n do" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 24 "\n p||j:=TT[i,j ]" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 13 "\n end do:" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 25 "\n TT[i,n+1]:=evalb(f)" }{MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 8 "\nend do;" }{MPLTEXT 1 0 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\"#\"\"%I%trueGI*protectedGF+" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\"$\"\"%I%tr ueGI*protectedGF+" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6# >&I#TTG6\"6$\"\"%F(I%trueGI*protectedGF*" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\"&\"\"%I%trueGI*protectedGF+" } {TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\"'\" \"%I%trueGI*protectedGF+" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\"(\"\"%I&falseGI*protectedGF+" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>&I#TTG6\"6$\"\")\"\"%I&fa lseGI*protectedGF+" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6 #>&I#TTG6\"6$\"\"*\"\"%I&falseGI*protectedGF+" }{TEXT 211 0 "" }}} {EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 9 "j:=2; pj;" }{MPLTEXT 1 209 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#>I\"jG6\"\"\"#" }{TEXT 211 0 "" }}{PARA 210 "" 1 "" {XPPMATH 20 "6#I#pjG6\"" }{TEXT 211 0 "" }}}{EXCHG {PARA 208 "> " 0 "" {MPLTEXT 1 209 0 "" }}}{EXCHG {PARA 213 "" 1 "" {TEXT 203 0 "" }}}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 214 "" 0 "" {TEXT 201 0 "" }}{PARA 215 "" 0 "" {TEXT 213 0 "" }}{PARA 216 "" 0 "" {TEXT 214 0 "" }}{PARA 216 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }