Simplify ¬(w∨(m∧¬w)) to ¬w∧¬m
So I'm just starting to get into Discrete Math and have overall had a good grasp on everything thus far, but this problem is wracking my brain. I've tried using different laws in different ways to try to work around this. I'm sure it's something simple, but I'm sure you guys have heard of zybooks that a lot of online classes use and it's not the most explanatory book in the world. So in a nutshell I'm looking for a bit of further explanation into finding this solution.
Much appreciated!
''wracking my brain'' interesting.
Simplify ¬(w∨(m∧¬w)) to ¬w∧¬m
$\neg(w\vee (m\wedge \neg w))$ gives by DeMorgan
$\neg w \wedge \neg (m\wedge \neg w)$ and by DeMorgan again
$\neg w \wedge (\neg m\vee w)$ and by distributivity
$(\neg w \wedge \neg m)\vee (\neg w \wedge w)$ and since $\neg w \wedge w$ is false,
$\neg w \wedge \neg m$ as claimed.