Is $((A\to B)\land (\lnot A \to C))\equiv (A\lor C)$?

Question

I'm wondering whether $((A\to B)\land (\lnot A \to C)) \iff (A\lor C)$ is correct or not.

Answer 1

Hint:

$\neg A \Rightarrow C$ is equivalent to $A\vee C$.

Answer 2

Hint: Consider the case $A:\text{true}$, $B:\text{false}$, $C:\text{any}$