What is the opposite of this expression?
$p \land ( q \lor r )$
Please suggest any theorem as a starting point.
What is the opposite of this expression?
$p \land ( q \lor r )$
Please suggest any theorem as a starting point.
Keep in mind that $\lnot (A\land B) = (\lnot A)\lor (\lnot B)$ and $\lnot (A\lor B) = (\lnot A)\land (\lnot B)$. Using this, you can figure out $\lnot (p \land ( q \lor r ))$ as follows: $\begin{eqnarray*}\lnot(p \land ( q \lor r )) &=& (\lnot p)\lor (\lnot(q\lor r))\\ &=& (\lnot p)\lor ((\lnot q)\land (\lnot r))\\\end{eqnarray*}$ which you can distribute out if you wish.