Expression $ ((A \oplus B) \land \lnot C) \lor (\lnot(A \oplus B) \land C)$ simplifies to $ A \oplus B \oplus C$ .
This is my attempt at simplification:
1. $ ((A \oplus B) \land \lnot C) \lor (\lnot(A \oplus B) \land C)$
2. $ (((A \land \lnot B) \lor (\lnot A \land B)) \land \lnot C) \lor (\lnot ((A \land \lnot B) \lor (\lnot A \land B)) \land C)$
3. $ ((\lnot C \land A \land \lnot B) \lor (\lnot C \land \lnot A \land B)) \lor (C \land \lnot A \land B) \lor (C \land A \land \lnot B)$
4. $ (\lnot A \land ((\lnot C \land B) \lor (C \land B))) \lor (\lnot B \land ((\lnot C \land A) \lor (C \land A))$
5. $ (\lnot A \land (B \land (\lnot C \lor C))) \lor (\lnot B \land (A \land (\lnot C \lor C)))$
6. $ (\lnot A \land B \land \top) \lor (\lnot B \land A \land \top)$
7. $ (\lnot A \land B) \lor (\lnot B \land A)$
8. $ A \oplus B$
What am I doing wrong? It looks to me like everything is correct, but my book says that $ A \oplus B \oplus C$ is the simplest form of this expression. If you know the correct way to simplify this, please write it in step by step form.
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