SOLUTION: lOGICS I can't figure out. Please help??? Fill in the heading of the following truth table using any of p, q, ~, , &#8596;, , and . Use keyboard shortcuts of --> for , <-->

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Question 321458: lOGICS
I can't figure out. Please help???
Fill in the heading of the following truth table using any of p, q, ~, , ↔, , and . Use keyboard shortcuts of --> for , <--> for ↔, V for , and ^ for .

p q ?
T T F
T F F
F T T
F F F
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


         p  q  ? 
case 1   T  T  F
case 2   T  F  F
case 3   F  T  T
case 4   F  F  F

Look for the case(s) where the unknown expression has truth value T

The only case in which the unknown expression has truth value T is case 3.

Case 3 is when p is false and q is true.

So we ask the question: 

"The simultaneous truths of what expressions 
cause the unknown expression to be true?

Answer: the simultaneous truths of ~p and q

So the unknown expression is ~p /\ q.

Checking with a truth table for ~p /\ q

         p  q  ~p  ~p /\ q
case 1   T  T   F     F
case 2   T  F   F     F
case 3   F  T   T     T
case 4   F  F   T     F

Edwin
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