document.write( "Question 321458: lOGICS\r
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\n" ); document.write( "\n" ); document.write( " 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 .\r
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\n" ); document.write( "p q ? \r
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Algebra.Com's Answer #230222 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "         p  q  ? \r\n" );
document.write( "case 1   T  T  F\r\n" );
document.write( "case 2   T  F  F\r\n" );
document.write( "case 3   F  T  T\r\n" );
document.write( "case 4   F  F  F\r\n" );
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document.write( "Look for the case(s) where the unknown expression has truth value T\r\n" );
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document.write( "The only case in which the unknown expression has truth value T is case 3.\r\n" );
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document.write( "Case 3 is when p is false and q is true.\r\n" );
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document.write( "So we ask the question: \r\n" );
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document.write( "\"The simultaneous truths of what expressions \r\n" );
document.write( "cause the unknown expression to be true?\r\n" );
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document.write( "Answer: the simultaneous truths of ~p and q\r\n" );
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document.write( "So the unknown expression is ~p /\ q.\r\n" );
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document.write( "Checking with a truth table for ~p /\ q\r\n" );
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document.write( "         p  q  ~p  ~p /\ q\r\n" );
document.write( "case 1   T  T   F     F\r\n" );
document.write( "case 2   T  F   F     F\r\n" );
document.write( "case 3   F  T   T     T\r\n" );
document.write( "case 4   F  F   T     F\r\n" );
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document.write( "Edwin
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