Prove $\sim$ (PV( $\sim$ p^q)) and $\sim$ P ^ $\sim q$ are logically equivalent by developing a series of logical equivalence.

solution :

Lets consider,

$\sim$ (pv ($\sim$ p ^ q))

= $\sim$ p ^ $\sim$ (\sim p ^ q) $\rightarrow$ Demorgan's Law

= $\sim$ p ^ p v $\sim$ …