Question 627978
Notice how the truth table for p ^ q has a last column of T, F, F, F


Flip everything to get F, F, F, T, which is exactly the last column in the given table above. 


So we go from p ^ q to ~(p ^ q)


Now use De Morgan's Law to simplify...


~(p ^ q)


<font color="red">~p V ~q</font>


So the full table is...


<TABLE BORDER=1>
<TR>
  <TD>p</TD>
  <TD>q</TD>
  <TD><font color="red">~p V ~q</font></TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>F</TD>
  <TD>F</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>F</TD>
  <TD>T</TD>
</TR>
</TABLE>



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