In propositional logic how is the negation equivalent?
First thing is to accept and understand, that $A \Rightarrow C$ is same as $(\neg A) \lor C$. Using your example we obtain, that &quot;If the battery is charged, then the phone is working&quot; is same with &quot;the battery is not charged or the phone is working&quot;.
Now following initial sentence $(A \land B) \Rightarrow C$ we have $\neg(A \land B) \lor C$, where last sounds as &quot;not fulfilling (the battery is charged and the screen is not cracked) or (the phone is working)&quot;.
Now we come to negation of $\neg(A \land B) = (\neg A) \lor (\neg B)$. So sentence &quot;not fulfilling (the battery is charged and the screen is not cracked)&quot; is same as &quot;(the battery is not charged) or  (the screen is cracked)&quot;
Putting everything together we have
$$(A \land B) \Rightarrow C \text{ is same with } (\neg A)  \lor (\neg B) \lor C $$
in words last is &quot;(the battery is not charged) or  (the screen is cracked) or (the phone is working)&quot;