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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.

an4s
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Angelica33
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  • https://math.stackexchange.com/questions/280844/using-the-distributivity-law-for-propositional-logic – an4s Mar 07 '18 at 20:27

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

aidangallagher4
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