Question 188797
You can use a truth table to prove this statement:


<table border="1"><tr><td>p</td><td>q</td><td>~p</td><td>~q</td><td>p v q</td><td>~(p v q)</td><td> ~p &amp; ~q</td></tr><tr><td>T</td><td>T</td><td>F</td><td>F</td><td>T</td><td><font color=red>F</font></td><td><font color=red>F</font></td></tr><tr><td>T</td><td>F</td><td>F</td><td>T</td><td>T</td><td><font color=red>F</font></td><td><font color=red>F</font></td></tr><tr><td>F</td><td>T</td><td>T</td><td>F</td><td>T</td><td><font color=red>F</font></td><td><font color=red>F</font></td></tr><tr><td>F</td><td>F</td><td>T</td><td>T</td><td>F</td><td><font color=red>T</font></td><td><font color=red>T</font></td></tr></table>



Notice how the columns in red have the same truth values. So this shows that the last columns are logically equivalent.