Technically this is math, but let's be honest, it's not.
I'm dead confused how to properly prove this. So while a simple solution will suffice, I would immensely appreciate an explanation along with it.
Show that ¬(p ∧ (¬p ∨ q)) and ¬p ∨ ¬q are equivalent by putting the following steps in order, top to bottom, to complete a series of logical equivalences, starting with ¬(p ∧ (¬p ∨ q)) and ending with ¬p ∨ ¬q, in which each step is an application of a fundamental equivalence.
The steps to be put in order are:
≡ T ∧ (¬p ∨ ¬q)
≡ (¬p ∨ p) ∧ (¬p ∨ ¬q)
≡ ¬p ∨ (p ∧ ¬q)
≡ (¬p ∨ ¬q) ∧ T
≡ ¬p ∨ (¬¬p ∧ ¬q)
≡ ¬p ∨ ¬(¬p ∨ q)