Question 452592
<pre>
Start out putting TTFF under the p's and TFTF under the q

(~p &#8897; q) &#8596; p
  T   T    T  
  T   F    T
  F   T    F
  F   F    F

Then under the ~ put the negation (opposite) of what's 
under the p.  That is <b>FFTT</b> and scratch what's under 
the p:

(~p &#8897; q) &#8596; p
 <b>F</b><s>T</s>   T    T  
 <b>F</b><s>T</s>   F    T
 <b>T</b><s>F</s>   T    F
 <b>T</b><s>F</s>   F    F

Then under the &#8897; put F if there are F's on both sides of
it and T the other times, then scratch through the columns on 
the sides of it.  That is, <b>TFTT</b>.


(~p &#8897; q) &#8596; p
 <s>F</s><s>T</s> <b>T</b> <s>T</s>    T  
 <s>F</s><s>T</s> <b>F</b> <s>F</s>    T
 <s>T</s><s>F</s> <b>T</b> <s>T</s>    F
 <s>T</s><s>F</s> <b>T</b> <s>F</s>    F

Then finally under the &#8596; put the T if it has the same 
thing on the left of it that it has on the right of it, and F
otherwise.  That is, put <b>TFFF</b>, and scratch through what's
on both sides of it:

(~p &#8897; q) &#8596; p
 <s>F</s>T <s>T</s> <s>T</s>  <b>T</b> <s>T</s>  
 <s>F</s>T <s>F</s> <s>F</s>  <b>F</b> <s>T</s>
 <s>T</s>F <s>T</s> <s>T</s>  <b>F</b> <s>F</s>
 <s>T</s>F <s>F</s> <s>F</s>  <b>F</b> <s>F</s>

The answer is <b>TFFF</b> which is also the
truth table for p&#8896;q, so the above
expression is equivalent to p&#8896;q.

Edwin</pre>