Simplify Implication Expression (Predicate/Prop Logic) I'm trying to do some past paper questions for revision and find myself perplexed on some of the expressions that need normalized/simplified which involves an implies.
For example:
(A ∧ ¬B) → B ∨ C ∨ ¬ (A ∧ ¬C) 
Now I know that A → B can be normalized to ¬A or B, but I can't seem to find an example when it comes to multiple things implying something to learn from.  I'd appreciate if someone could explain to me how I would simplify such an expression.

The rule that you cite:
$$A \rightarrow B = \neg A \vee B$$
also works when $A$ is a compound expression. (All of these rules do). In your example, the simplification would go like this:
$$
\begin{aligned}
(A \wedge \neg B) &\rightarrow B \vee C \vee \neg(A \wedge \neg C)\\
\neg(A \wedge \neg B) &\vee (B \vee C \vee \neg(A \wedge \neg C))\\
\neg A \vee \neg \neg B &\vee B \vee C \vee \neg(A \wedge \neg C)\\
\neg A \vee B &\vee B \vee C \vee \neg A \vee \neg \neg C\\
\neg A &\vee B \vee C\\
\end{aligned}
$$
Here I've used DeMorgan's laws twice.
