document.write( "Question 1190254: Topics In Contemporary Math\r
\n" ); document.write( "\n" ); document.write( " Arguments\r
\n" ); document.write( "\n" ); document.write( "Use truth tables to determine if each of the following arguments are valid or invalid.\r
\n" ); document.write( "\n" ); document.write( "3) I will not wear a Speedo at the beach or I will be embarrassed.
\n" ); document.write( "I am not embarrassed.
\n" ); document.write( "Therefore, I did not wear a Speedo at the beach. \n" ); document.write( "
Algebra.Com's Answer #821861 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Always let letters represent the positive idea, not the negative idea.\r\n" );
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document.write( "Let S = \"I will wear a Speedo at the beach\"\r\n" );
document.write( "Let E = \"I will be embarrassed\"

\n" ); document.write( "I will not wear a Speedo at the beach or I will be embarrassed.
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document.write( "That's the 1st premise:  ~S ∨ E

\n" ); document.write( "I am not embarrassed.
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document.write( "That's the 2nd premise:  ~E

\n" ); document.write( "Therefore, I did not wear a Speedo at the beach.
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document.write( "That's the conclusion:  ~S\r\n" );
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document.write( "That written in symbols is   [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
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document.write( "Put ● between the premises and ⊃ between the set of premises \r\n" );
document.write( "and the conclusion.\r\n" );
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document.write( "Put \"not\" (negation) indicated by ~ before the positive \r\n" );
document.write( "premises if necessary to make them negative \r\n" );
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document.write( "Put TTFF under each S and TFTF under each E\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "     T   T      T      T\r\n" );
document.write( "     T   F      F      T\r\n" );
document.write( "     F   T      T      F\r\n" );
document.write( "     F   F      F      F\r\n" );
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document.write( "Under each ~ put the opposite of what follows it. That is,\r\n" );
document.write( "if a T follows the ~ put an F under the ~, and if an F \r\n" );
document.write( "follows the ~, put a T under the.\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "    FT   T     FT     FT\r\n" );
document.write( "    FT   F     TF     FT\r\n" );
document.write( "    TF   T     FT     TF\r\n" );
document.write( "    TF   F     TF     TF\r\n" );
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document.write( "Erase what followed the ~\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "    F    T     F      F \r\n" );
document.write( "    F    F     T      F \r\n" );
document.write( "    T    T     F      T\r\n" );
document.write( "    T    F     T      T\r\n" );
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document.write( "Under the ∨ put F only if there are F's\r\n" );
document.write( "immediately on BOTH sides of the ∨.  \r\n" );
document.write( "Otherwise put a T.\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "    F  T T     F      F \r\n" );
document.write( "    F  F F     T      F \r\n" );
document.write( "    T  T T     F      T\r\n" );
document.write( "    T  T F     T      T\r\n" );
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document.write( "Erase what the ∨ was between\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "       T       F      F \r\n" );
document.write( "       F       T      F \r\n" );
document.write( "       T       F      T\r\n" );
document.write( "       T       T      T\r\n" );
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document.write( "Under the ● (and) put T only if there are T's \r\n" );
document.write( "immediately on BOTH sides of the ●.  Otherwise \r\n" );
document.write( "put a F.\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "       T    F  F      F \r\n" );
document.write( "       F    F  T      F \r\n" );
document.write( "       T    F  F      T\r\n" );
document.write( "       T    T  T      T\r\n" );
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document.write( "Erase what the ● was between:\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "            F         F \r\n" );
document.write( "            F         F \r\n" );
document.write( "            F         T\r\n" );
document.write( "            T         T\r\n" );
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document.write( "Under the ⊃ (conditional (if-then) put F only \r\n" );
document.write( "if there is a T on the LEFT of the ⊃ and an F \r\n" );
document.write( "on the RIGHT.  Otherwise put a T.\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\r\n" );
document.write( "  ----------------------- \r\n" );
document.write( "            F      T   F    \r\n" );
document.write( "            F      T   F \r\n" );
document.write( "            F      T   T\r\n" );
document.write( "            T      T   T\r\n" );
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document.write( "Erase what the ⊃ was between\r\n" );
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document.write( "  [(~S ∨ E) ●  ~E] ⊃  ~S\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" );
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document.write( "This tells us the argument is totally valid.\r\n" );
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document.write( "If you are left with a line of all T's, the\r\n" );
document.write( "argument is valid.  If there had been any F's,\r\n" );
document.write( "it would only be conditionally valid.\r\n" );
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document.write( "[Notice we started with T's and F's under the letters\r\n" );
document.write( "only, and then got them all under the symbols and none\r\n" );
document.write( "under the letters, then we ended up with only one column.\r\n" );
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document.write( "Edwin
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