Consider the logic equation below:
$$(\lnot A \land B \land \lnot C) \lor (A \land \lnot B \land C)$$
It is already in Disjunctive Normal Form. I'm wondering if there is any way to simplify the equation further. Since $A,B,C$ are all the negations of themselves in each of the individual brackets I don't think there are any simpler ways of writing this, but I'm not sure.
If there is a more simplified version, can someone please let me know and how to reach such a simplified form.
Thanks in advance!
Best Answer
It's already in its simplest form.
Generally if you write it the "arithmetic way" i.e. $$A'BC'+AB'C$$ you see that you cannot really find something nicer since you cannot factor anything.
While if was written as product of sums $$(A+B+C)(A+B+C')(A+B'+C')(A'+B+C)(A'+B'+C)(A'+B'+C')$$
you might think with reason that expanding it would lead to simplifications.
Note: you can play with the software Logic Friday to evaluate these kind of expressions.