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For variables use p1, p2, . . . , pn. You may als o use iff as a connective by writing " }{TEXT 205 8 "p iff q " }{TEXT 203 3 "as " }{TEXT 205 8 "iff(p,q)" }{TEXT 203 1 "." }{TEXT 203 0 "" } }{PARA 203 "> " 0 "" {MPLTEXT 1 0 127 "f:=((p1 implies p2) and (p2 imp lies p3) and (p3 implies p1)) implies ((p1 implies p3) and (p2 implies p3) and (p3 implies p1));" }{MPLTEXT 1 0 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"nG6\"\"\"$" }{TEXT 206 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"h33hI#p1GF%I#p2GF%hF+I#p3GF%hF-F*33hF*F-F,F." }{TEXT 206 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 1 ";" } {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 96 "T T:=Array(1..1+2^n,1..1+n): #Create an array of the appropriate dimens ions for the truth-table." }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 47 "for j from 1 to n do #Title the truth-ta ble." }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 41 "\n TT[1,j]:=cat(\"p \",convert(j,string))" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 8 "\nend d o:" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 26 "prop:=convert(f,string): " }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 19 "if length(prop)>115" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 25 "\n then TT[1,n+1]:=\"f\"" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 27 "\n else TT[1,n+1]:=prop " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 9 "\nend if: " }{MPLTEXT 1 204 0 "" }}} {EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 92 "for j from 1 to n do \+ #For all the independent variable entries in the array enter false." }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 30 "\n for i from 2 to 2^n+1 \+ do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 27 "\n TT[i,j]:=fa lse" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 12 "\n end do" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 8 "\nend do:" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 72 "for j from 1 to n do #In each column enter the initial block of T's." }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 30 "\n for i from 2 to 2^n+1 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 47 "\n if i-1<=2^(n-j) then TT[i,j] :=true " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 12 "\n end if" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 12 "\n end do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 18 "\nend do: " }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 88 "for j from 1 to n do #Extend the initial block of T's & F's to the rest of the column." }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 40 "\n for i from 2+2^(n-j+1) to 1+2^n do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 42 "\n \+ for k from 2 to 1+2^(n-j) do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 79 "\n if i mod 2^(n-j+1) = k mod 2^(n-j+1) then TT[i, j]:=TT[k,j]" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 26 "\n \+ end if" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 20 "\n e nd do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 12 "\n end do" } {MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 17 "\nend do: " }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 203 "> " 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 "" }}}{EXCHG {PARA 202 "> \+ " 0 "" {MPLTEXT 1 204 56 "if length(prop)>115 then print(\"f = \"||pro p) end if; TT;" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 " 6#Qfrf~=~(p1~implies~p2)~and~(p2~implies~p3)~and~(p3~implies~p1)~impli es~(p1~implies~p3)~and~(p2~implies~p3)~and~(p3~implies~p1)6\"" }{TEXT 206 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#-I'RTABLEG6\"6%\"'!QR&-I'M ATRIXGF%6#7+7&Q#p1F%Q#p2F%Q#p3F%Q\"fF%7&I%trueGI*protectedGF3F2F2F27&F 2F2I&falseGF3F27&F2F5F2F27&F2F5F5F27&F5F2F2F27&F5F2F5F27&F5F5F2F27&F5F 5F5F2I&ArrayGF3" }{TEXT 206 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 139 "If n>3, then a small rectangle appears in lieu of the truth-t able. 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