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
Here's an alternative.
$$ \begin{align} A \leftrightarrow (B \lor C) &\equiv [\lnot A \land \lnot(B \lor C)] \lor [A \land(B \lor C)] \\ &\equiv ( \lnot A \land \lnot B \land \lnot C) \lor ( A \land [(\lnot B \land C) \lor (B \land\lnot C) \lor (B \land C)]) \\ &\equiv ( \lnot A \land \lnot B \land \lnot C) \lor (A \land \lnot B \land C) \lor (A \land B \land \lnot C) \lor (A \land B \land C) \end{align} $$