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Is it possible to write following expression with each variable occuring only 1 time and using any of operations $\land\neg\lor\oplus$ ?

$$(A\land\neg C)\lor(B\land C)$$

Somnium
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  • Sorry if I'm not helpful, but you want each variable to occur only once and to have each of the 4 operators occur only once also? So excluding the $\neg$ operator you have 3 variables and only to positions for the operators. Something like this: $A?B?C$, where ? is one of the 3 operators $\land\lor\oplus$. Of course you can put $\neg$ in 4 positions , but putting the other 3 operator in before the first variable, or after the last one those not make much sense. Of course I'm not very good with these logical statements , and I maybe haven't understood your question right. – randomname Jul 04 '14 at 10:49
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    @randomname I think the problem as written does not require the operations to appear only once each, only the variable names $A,B,C$. – coffeemath Jul 04 '14 at 11:05
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    @randomname I meant only variables each once, operators any of listed in various count. – Somnium Jul 04 '14 at 11:16
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    I don't know if this helps but...

    That is equivalent to

    $ \neg(\neg A \lor C) \lor (B \land C)$

    $ \equiv \neg(A \to C) \lor (B \land C)$

    $ \equiv (A \to C) \to (B \land C)$

     – BCLC Jul 04 '14 at 12:53

1 Answers1

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By brute enumeration it can be verified that no such formula exists.

Karolis Juodelė
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