document.write( "Question 1183316: Find the truth value of each of the
\n" ); document.write( "following compound propositions by constructing a truth table: 1. ~(p^q) 2. ~pV~q 3. (p^q)→(pV~q) 4. (p→~p)↔q 5. ~q→(p↔r) \n" ); document.write( "
Algebra.Com's Answer #813576 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You just need to learn to use the rules for placing T's and F's\r\n" );
document.write( "under the columns with ~, ^, v, →, ↔\r\n" );
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document.write( "Rules for putting T or F:\r\n" );
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document.write( "~T becomes F, ~F becomes T\r\n" );
document.write( "T^T becomes T, anything else with ^ becomes F\r\n" );
document.write( "FvF becomes F, anything else with v becomes T\r\n" );
document.write( "T→F becomes F, anything else with → becomes T\r\n" );
document.write( "T↔T, F↔F both become T, anything else with ↔ becomes F  \r\n" );
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document.write( "Now you fill in the missing T's, F's by the rules above\r\n" );
document.write( "I've filled the T's and F's under the columns for the\r\n" );
document.write( "single letters p, q, r.\r\n" );
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document.write( "1.  ~(p^q) \r\n" );
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document.write( " p | q | p^q | ~(p^q) |\r\n" );
document.write( " T | T |     |        |\r\n" );
document.write( " T | F |     |        |\r\n" );
document.write( " F | T |     |        |\r\n" );
document.write( " F | F |     |        |\r\n" );
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document.write( "2.  ~pv~q    \r\n" );
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document.write( " p | q | ~p | ~q | ~pV~q) |\r\n" );
document.write( " T | T |    |    |        |\r\n" );
document.write( " T | F |    |    |        |\r\n" );
document.write( " F | T |    |    |        |\r\n" );
document.write( " F | F |    |    |        |\r\n" );
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document.write( "3.  (p^q)→(pV~q)  \r\n" );
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document.write( " p | q | r | ~q | p^q | pV~q | (P^q)→(pV~q) |\r\n" );
document.write( " T | T | T |    |     |      |              |\r\n" );
document.write( " T | T | F |    |     |      |              |\r\n" );
document.write( " T | F | T |    |     |      |              |\r\n" );
document.write( " T | F | F |    |     |      |              |\r\n" );
document.write( " F | T | T |    |     |      |              |\r\n" );
document.write( " F | T | F |    |     |      |              |\r\n" );
document.write( " F | F | T |    |     |      |              |\r\n" );
document.write( " F | F | F |    |     |      |              |\r\n" );
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document.write( "4. ~q→(p↔r)\r\n" );
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document.write( " p | q | r | ~q | p↔r | ~q→(p↔r) |\r\n" );
document.write( " T | T | T |    |     |          |              \r\n" );
document.write( " T | T | F |    |     |          |              \r\n" );
document.write( " T | F | T |    |     |          |              \r\n" );
document.write( " T | F | F |    |     |          |              \r\n" );
document.write( " F | T | T |    |     |          |              \r\n" );
document.write( " F | T | F |    |     |          |              \r\n" );
document.write( " F | F | T |    |     |          |              \r\n" );
document.write( " F | F | F |    |     |          |              \r\n" );
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document.write( "Edwin

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