document.write( "Question 208804: Determine the truth value of the statement ~q <-> [~ r ~ (p ^ q)] when p is false, q is true, and r is true \n" ); document.write( "
Algebra.Com's Answer #157925 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There are 8 building blocks for ~q <-> [~r^(pvq)] \r\n" );
document.write( "so that each successive one can be gotten by\r\n" );
document.write( "doing negation, disjunction, conjunction, and \r\n" );
document.write( "biconditional operations on one or two previous\r\n" );
document.write( "building blocks, starting with the single letters: \r\n" );
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document.write( "        ~q <-> [~r^(pvq)]            \r\n" );
document.write( "                                 \r\n" );
document.write( "1                   p                start with 1st single letter\r\n" );
document.write( "2        q                           2nd single letter\r\n" );
document.write( "3                r                   3rd single letter\r\n" );
document.write( "4               ~r                   the negation of 3\r\n" );
document.write( "5                  (pvq)             the disjunction of 1,2\r\n" );
document.write( "6              [~r^(pvq)]            the conjunction of 4,5\r\n" );
document.write( "7       ~q                           the negation of 2\r\n" );
document.write( "8       ~q <-> [~r^(pvq)]            the biconditional of 6 and 7\r\n" );
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document.write( "Make a chart:\r\n" );
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document.write( " p    q   r   ~r   (pvq) [~r^(pvq)]   ~q    ~q <-> [~r^(pvq)]\r\n" );
document.write( " |    |   |    |     |      |          |        |   \r\n" );
document.write( " F    T   T    F     T      F          F        T\r\n" );
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document.write( "So the truth value is T.\r\n" );
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document.write( "Edwin
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