I'm in the process of minimizing a boolean equation, and I've gotten it into the following form:
$$\lnot B \lor (B \land \lnot C) \lor C$$
Just by looking at it, I can tell that this is always TRUE. The complements of the center term are covered by the other two. However, I can't quite prove it formally.
I can split the middle term using indempotency:
$$\lnot B \lor (B \land \lnot C) \lor (B \land \lnot C) \lor C$$
Then (again, intuitively) I can tell that the two left terms simplify to: $\lnot B \land \lnot C$
What is the rule (or rules) that can get the left two terms into this form? Once I know that rule, I can formally solve the equation like so:
$$ \lnot B \lor \lnot C \lor C\lor B$$ $$(\lnot B \lor B) \lor (\lnot C \lor C)$$ $$ 1$$
Any help would be greatly appreciated!