Prove $\overline{A}\cap \left(A \cup \overline{B}\right) = \overline{A \cup B}$

Question

How can I prove $$\overline{A}\cap \left(A \cup \overline{B}\right) = \overline{A \cup B}$$ with boolean algebra? Honestly, I have absolutely no clue on how to do it. Any help would be greatly appreciated, I have been staring at this for hours and I just can't wrap my mind around how to solve it and what the answer is.

Answer 1

$$\begin{align*} A’\cap(A\cup B’) & = (A’\cap A) \cup (A’ \cap B’)\tag{distributive law}\\ & = \emptyset \cup (A’ \cap B’)\\ & = (A’ \cap B’)\\ & = (A\cup B)’\tag{de Morgan} \end{align*} $$