Simplifying a Boolean Expression 2

Question

The boolean expression is as follows: (¬A^¬B^¬C)∨(A^¬B^C)∨(A^B^¬C)∨(A^B^C)

I have found that A⊕(¬B^¬C) is equal to the above but I have absolutely no idea on how to get this result, I have spent hours simplifying the above expression and time and time again have drawn blanks.

Any help would be greatly appreciated

Yes, but I have to show the steps taken to find the finished result — Paul Shirebrook, Nov 21 '14 at 01:40

score 0 · Accepted Answer · answered Nov 21 '14 at 01:29

0

Here's an alternative.

$$ \begin{align} A \leftrightarrow (B \lor C) &\equiv [\lnot A \land \lnot(B \lor C)] \lor [A \land(B \lor C)] \\ &\equiv ( \lnot A \land \lnot B \land \lnot C) \lor ( A \land [(\lnot B \land C) \lor (B \land\lnot C) \lor (B \land C)]) \\ &\equiv ( \lnot A \land \lnot B \land \lnot C) \lor (A \land \lnot B \land C) \lor (A \land B \land \lnot C) \lor (A \land B \land C) \end{align} $$

answered Nov 21 '14 at 01:29

Mike

103

Thank you for the response, I have no experience in using '↔' but I will look into it. – Paul Shirebrook Nov 21 '14 at 01:44
Threw me off, I have used ENOR before, thank you so much for the help. – Paul Shirebrook Nov 21 '14 at 02:08

Simplifying a Boolean Expression 2

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