document.write( "Question 516109: Determine which, if any, of the three statements are equivalent.
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\n" ); document.write( "III) Either my car starts or I will make it to work on time. \n" ); document.write( "
Algebra.Com's Answer #344251 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let s = \"My car does not start.\"\r\n" );
document.write( "Let w = \"I will make it to work on time.\"\r\n" );
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document.write( "I) If my car does not start, then I will not make it to work on time.\r\n" );
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document.write( "That's ~s->~w\r\n" );
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document.write( "s  w  ~s  ~w  ~s -> ~w\r\n" );
document.write( "T  T   F   F      T\r\n" );
document.write( "T  F   F   T      T\r\n" );
document.write( "F  T   T   F      F\r\n" );
document.write( "F  F   T   T      T\r\n" );
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document.write( "II) If my car does not start, then I will make it to work on time.\r\n" );
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document.write( "That's ~s -> w\r\n" );
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document.write( "s  w  ~s  ~s -> w\r\n" );
document.write( "T  T   F     T\r\n" );
document.write( "T  F   F     T\r\n" );
document.write( "F  T   T     T\r\n" );
document.write( "F  F   T     F\r\n" );
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document.write( "III) Either my car starts or I will make it to work on time.\r\n" );
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document.write( "That's s V w\r\n" );
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document.write( "s  w  s V w\r\n" );
document.write( "T  T    T\r\n" );
document.write( "T  F    T    \r\n" );
document.write( "F  T    T    \r\n" );
document.write( "F  F    F    \r\n" );
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document.write( "II and III are equivalent because they have the same truth table,\r\n" );
document.write( "TTTF.  \r\n" );
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document.write( "Or you can prove it because \r\n" );
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document.write( "(p->q) <=> (~pVq) \r\n" );
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document.write( "Let p = ~s and q = w, then\r\n" );
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document.write( "(~s->w) <=> (~(~s) V w)\r\n" );
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document.write( "(~s->w) <=> (s V w)\r\n" );
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document.write( "Edwin
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