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I am no expert on Boolean logic, but this may be some start for you: homework = Implies[r, b] && Implies[r, Implies[b, f]] && Implies[b, Implies[f, h]] BooleanConvert[homework] LogicalExpand[homework] BooleanTable[homework, {r, b, f, h}] You could check the documentation and the examples of these functions.


If you want recursion, write recursively. dualF[Not[p_]] := Not[dualF[p]] dualF[And[p_, q_]] := Not[Or[Not[dualF[p]], Not[dualF[q]]]] dualF[Or[p_, q_]] := Not[And[Not[dualF[p]], Not[dualF[q]]]] dualF[p_Symbol] := p then dualF[p && (q || r)] ! (! p || (! q && ! r)) which has the truth table which is same as

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