Question 588459
# 1

<TABLE BORDER=1>
<TR>
  <TD>p</TD>
  <TD>q</TD>
  <TD>~p</TD>
  <TD>~p -> q</TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>T</TD>
  <TD>F</TD>
  <TD>T</TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>F</TD>
  <TD>F</TD>
  <TD>T</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>T</TD>
  <TD>T</TD>
  <TD>T</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>F</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>

</TABLE>


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# 2

<TABLE BORDER=1>
<TR>
  <TD>p</TD>
  <TD>q</TD>
  <TD>p -> q</TD>
  <TD>~(p -> q)</TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>T</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>
<TR>
  <TD>T</TD>
  <TD>F</TD>
  <TD>F</TD>
  <TD>T</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>T</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>
<TR>
  <TD>F</TD>
  <TD>F</TD>
  <TD>T</TD>
  <TD>F</TD>
</TR>
</TABLE>


Notes:

1) ~p is the opposite of p. So if p is true, then ~p is false. If p is false, then ~p is true.


2) p -> q is only false when both p is true and q is false. Otherwise, p -> q is true.