logic proposition simplify version

Question

I want to know the simplify version of

$((((A => B) | A) \& \sim B) => f)$

is $( \sim A V B) $?

or

$((A V B) \& ( \sim A V B))$ ?

Answer 1

$$(((A \Rightarrow B) \lor A)\land \neg B)$$ $$(((\neg A \lor B) \lor A)\land \neg B)$$ $$(((\neg A \lor A) \lor B)\land \neg B)$$ $$(((\neg A \lor A) \lor B)\land \neg B)$$ $$(B \land \neg B)$$ $$\text{False}$$