document.write( "Question 1197292: Construct a Truth Table for ~(𝑷𝜦~𝑸) : The Negation of the Conjunction of P and the Negation of Q \n" ); document.write( "
Algebra.Com's Answer #830713 by Edwin McCravy(20056)\"\" \"About 
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document.write( "~(𝑷𝜦~𝑸) from inner to outer has parts 𝑷, 𝑸, ~𝑸, 𝑷𝜦~𝑸, ~(𝑷𝜦~𝑸) \r\n" );
document.write( "Now make a chart for lists of T's and F's under each part:\r\n" );
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document.write( "| 𝑷 | 𝑸 | ~𝑸 | 𝑷𝜦~𝑸 | ~(𝑷𝜦~𝑸)| \r\n" );
document.write( "|   |    |    |       |         |\r\n" );
document.write( "|   |    |    |       |         |\r\n" );
document.write( "|   |    |    |       |         |\r\n" );
document.write( "|   |    |    |       |         |\r\n" );
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document.write( "Start by putting TTFF under the first letter P and TFTF under the second\r\n" );
document.write( "letter Q\r\n" );
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document.write( "| 𝑷 | 𝑸 | ~𝑸 | 𝑷𝜦~𝑸 | ~(𝑷𝜦~𝑸)| \r\n" );
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( "Now fill in the column under ~𝑸 according to the rule, if 𝑸 on that line \r\n" );
document.write( "has T, put F under ~𝑸 on that line,  If 𝑸 on that line has F, put T under\r\n" );
document.write( " ~𝑸.\r\n" );
document.write( "\r\n" );
document.write( "| 𝑷 | 𝑸 | ~𝑸 | 𝑷𝜦~𝑸 | ~(𝑷𝜦~𝑸)| \r\n" );
document.write( "| T | T  | F  |       |         |\r\n" );
document.write( "| T | F  | T  |       |         |\r\n" );
document.write( "| F | T  | F  |       |         |\r\n" );
document.write( "| F | F  | T  |       |         |\r\n" );
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document.write( "𝑷𝜦~𝑸 is made up of 𝑷, ~𝑸, and 𝜦 between them. Rule:  if 𝑷 and ~𝑸 both \r\n" );
document.write( "have T's on that line, then put T under 𝑷𝜦~𝑸, but if either one is F, then \r\n" );
document.write( "put F.\r\n" );
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document.write( "| 𝑷 | 𝑸 | ~𝑸 | 𝑷𝜦~𝑸 | ~(𝑷𝜦~𝑸)| \r\n" );
document.write( "| T | T  | F  |  F    |         |\r\n" );
document.write( "| T | F  | T  |  T    |         |\r\n" );
document.write( "| F | T  | F  |  F    |         |\r\n" );
document.write( "| F | F  | T  |  F    |         |\r\n" );
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document.write( "Now fill in the column under ~(𝑷𝜦~𝑸) according to the rule, if 𝑷𝜦~𝑸 on that\r\n" );
document.write( "line has T, put F under ~(𝑷𝜦~𝑸) on that line,  If 𝑷𝜦~𝑸 on that line has F, \r\n" );
document.write( "put T under ~(𝑷𝜦~𝑸)\r\n" );
document.write( "\r\n" );
document.write( "| 𝑷 | 𝑸 | ~𝑸 | 𝑷𝜦~𝑸 | ~(𝑷𝜦~𝑸)| \r\n" );
document.write( "| T | T  | F  |  F    |    T    |\r\n" );
document.write( "| T | F  | T  |  T    |    F    |\r\n" );
document.write( "| F | T  | F  |  F    |    T    |\r\n" );
document.write( "| F | F  | T  |  F    |    T    |\r\n" );
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document.write( "Edwin
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