document.write( "Question 451893: if p is true, q is false, and r is true, find the truth value of the statement.
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Algebra.Com's Answer #310692 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Start with this putting TTFF under p and TFTF under q \r\n" );
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document.write( "p  q  ~p  ~q   ∼p∨q  (∼p∨q)→ ∼q\r\n" );
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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( "Under the ~p put the opposite of p. Since p has TTFF,\r\n" );
document.write( "~p will have FFTT:\r\n" );
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document.write( "p  q  ~p  ~q  ∼p∨q  (∼p∨q)→ ∼q\r\n" );
document.write( "覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "T  T   F\r\n" );
document.write( "T  F   F\r\n" );
document.write( "F  T   T\r\n" );
document.write( "F  F   T\r\n" );
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document.write( "Under the ~q put the opposite of q. Since q has TFTF,\r\n" );
document.write( "~q will have FTFT:\r\n" );
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document.write( "p  q  ~p  ~q  ∼p∨q  (∼p∨q)→ ∼q\r\n" );
document.write( "覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "T  T   F   F\r\n" );
document.write( "T  F   F   T\r\n" );
document.write( "F  T   T   F \r\n" );
document.write( "F  F   T   T\r\n" );
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document.write( "We make ∼p∨q out of the columns ~p, q according to\r\n" );
document.write( "the rule:\r\n" );
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document.write( "If there are F's on both sides of the disjunction\r\n" );
document.write( "symbol ∨ the disjunction is F, otherwise it's T\r\n" );
document.write( "Since ~p is FFTT and q is TFTF, then only the 2nd \r\n" );
document.write( "row has F under both ~q and p, so it gets F and the\r\n" );
document.write( "other three get T, so under ∼p∨q we put TFTT\r\n" );
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document.write( "p  q  ~p  ~q  ∼p∨q  (∼p∨q)→ ∼q\r\n" );
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document.write( "T  T   F   F    T \r\n" );
document.write( "T  F   F   T    F\r\n" );
document.write( "F  T   T   F    T\r\n" );
document.write( "F  F   T   T    T\r\n" );
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document.write( "We make (∼p∨q)→∼q out of the columns ∼p∨q and ∼q according to\r\n" );
document.write( "the rule:\r\n" );
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document.write( "If there is a T on the left of the conditional \r\n" );
document.write( "symbol → and a T on the right side of the conditional\r\n" );
document.write( "symbol, the conditional is F, otherwise it's T.\r\n" );
document.write( "Since ∼p∨q is TFTT and ~q is FTFT, then the 1st \r\n" );
document.write( "and 3rd rows has F have this, so it gets F in rows\r\n" );
document.write( "1 and 3\r\n" );
document.write( "other two get T, so under (∼p∨q)→ ∼q\r\n" );
document.write( "we put FTFT\r\n" );
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document.write( "p  q  ~p  ~q  ∼p∨q  (∼p∨q)→ ∼q\r\n" );
document.write( "覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "T  T   F   F    T         F \r\n" );
document.write( "T  F   F   T    F         T\r\n" );
document.write( "F  T   T   F    T         F\r\n" );
document.write( "F  F   T   T    T         T\r\n" );
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document.write( "Edwin
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