document.write( "Question 539617: I have to make the following compound statement into a truth table and i do not understand how to construct the table.\r
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Algebra.Com's Answer #353497 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The parts that make up that expression q V (p -> ~r)  are \r\n" );
document.write( "p, q, r, ~r, (p -> ~r),  and q V (p -> ~r).  Make a heading for each of these.\r\n" );
document.write( "When there are three variables, the truth table will have 8 rows.\r\n" );
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document.write( "Start with this:\r\n" );
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document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
document.write( "  |   |   |    |           | \r\n" );
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document.write( "Fill in the p column with the first half T's and last half F's\r\n" );
document.write( "\r\n" );
document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "T |   |   |    |           | \r\n" );
document.write( "T |   |   |    |           | \r\n" );
document.write( "T |   |   |    |           | \r\n" );
document.write( "T |   |   |    |           | \r\n" );
document.write( "F |   |   |    |           | \r\n" );
document.write( "F |   |   |    |           | \r\n" );
document.write( "F |   |   |    |           | \r\n" );
document.write( "F |   |   |    |           |\r\n" );
document.write( "\r\n" );
document.write( "Fill in the q column with 2 T's, 2 F's, 2 T's, 2 F's:\r\n" );
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document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "T | T |   |    |           | \r\n" );
document.write( "T | T |   |    |           | \r\n" );
document.write( "T | F |   |    |           |\r\n" );
document.write( "T | F |   |    |           | \r\n" );
document.write( "F | T |   |    |           |\r\n" );
document.write( "F | T |   |    |           |  \r\n" );
document.write( "F | F |   |    |           |\r\n" );
document.write( "F | F |   |    |           |\r\n" );
document.write( "\r\n" );
document.write( "Fill in the r-column alternating T,F,T,F,T,F,T,F \r\n" );
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document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\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" );
document.write( "\r\n" );
document.write( "Fill in the ~r column as the opposite of the r column\r\n" );
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document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "T | T | T |  F |           | \r\n" );
document.write( "T | T | F |  T |           | \r\n" );
document.write( "T | F | T |  F |           |\r\n" );
document.write( "T | F | F |  T |           | \r\n" );
document.write( "F | T | T |  F |           |\r\n" );
document.write( "F | T | F |  T |           |  \r\n" );
document.write( "F | F | T |  F |           |\r\n" );
document.write( "F | F | F |  F |           |\r\n" );
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document.write( "Fill in the (p -> ~r) column by this rule:  If the\r\n" );
document.write( "p column has a T and the ~r column has a F, then put\r\n" );
document.write( "an F in the (p -> ~r) column; otherwise put a T.\r\n" );
document.write( "\r\n" );
document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "T | T | T |  F |     F     | \r\n" );
document.write( "T | T | F |  T |     T     | \r\n" );
document.write( "T | F | T |  F |     F     |\r\n" );
document.write( "T | F | F |  T |     T     | \r\n" );
document.write( "F | T | T |  F |     T     |\r\n" );
document.write( "F | T | F |  T |     T     |  \r\n" );
document.write( "F | F | T |  F |     T     |\r\n" );
document.write( "F | F | F |  F |     T     |\r\n" );
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document.write( "Fill in the q V (p -> ~r) by this rule:\r\n" );
document.write( "If both the q column and the (p -> ~r) column\r\n" );
document.write( "have F's, then put an F in the q V (p -> ~r)\r\n" );
document.write( "column; otherwise put T.\r\n" );
document.write( "\r\n" );
document.write( "p | q | r | ~r | (p -> ~r) | q V (p -> ~r)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "T | T | T |  F |     F     |      T \r\n" );
document.write( "T | T | F |  T |     T     |      T\r\n" );
document.write( "T | F | T |  F |     F     |      F\r\n" );
document.write( "T | F | F |  T |     T     |      T\r\n" );
document.write( "F | T | T |  F |     T     |      T\r\n" );
document.write( "F | T | F |  T |     T     |      T\r\n" );
document.write( "F | F | T |  F |     T     |      T\r\n" );
document.write( "F | F | F |  F |     T     |      T\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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