document.write( "Question 1073790: I can understand the truth table, here is the formula -- (pvq)^~p
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Algebra.Com's Answer #688593 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "You must learn the rules for \"not\", \"or\" and \"and\".\r\n" );
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document.write( "\"Not\" is denoted by ~.  It only precedes a letter.\r\n" );
document.write( "It is FALSE whenever what follows it is TRUE, and\r\n" );
document.write( "it is TRUE whenever what follows it is FALSE.\r\n" );
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document.write( "\"or\" must be between two letters.\r\n" );
document.write( "\"Or\" is denoted by \"v\", It is FALSE ONLY when there\r\n" );
document.write( "are FALSEs on BOTH SIDES of it; otherwise it is TRUE.\r\n" );
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document.write( "\"And\" also must be between two letters.\r\n" );
document.write( "\"And\" is denoted by \"^\", It is TRUE ONLY when there\r\n" );
document.write( "are TRUEs on BOTH SIDES of it; otherwise it is FALSE.\r\n" );
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document.write( "To make a truth table when there are two letters, put \r\n" );
document.write( "TTFF under all the p's like this\r\n" );
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document.write( "Then put TFTF under all q's (in this example there's only \r\n" );
document.write( "one q):\r\n" );
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document.write( "Now that we have a list of T's and F's under each letter,\r\n" );
document.write( "we are ready to start putting a list of T's and F's under\r\n" );
document.write( "the symbols, using the rules above.\r\n" );
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document.write( "We can put a list under the v because there is a list on\r\n" );
document.write( "both sides of it, but we must wait to put a list under the \r\n" );
document.write( "^, because we must complete the parentheses first.\r\n" );
document.write( "So we put TTTF under the v, like this: (I explain why\r\n" );
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document.write( "The reason we put T's on the first three lines\r\n" );
document.write( "and an F on the bottom line under the \"v\" is because \r\n" );
document.write( "only the bottom line has F's on both sides of the \r\n" );
document.write( "\"v\" column. Rmember that \"v\" get an F only when\r\n" );
document.write( "there are F's on both sides of the \"v\" column.\r\n" );
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document.write( "Since we have used the lists on each side of the \"v\",\r\n" );
document.write( "we can erase them or cross them out, for we don't need\r\n" );
document.write( "them anymore.  Or we can leave them there and just\r\n" );
document.write( "ignore them.  I'll cross them out.\r\n" );
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document.write( "Next we put a list under the ~, using the rule it is an F\r\n" );
document.write( "if it precedes a T and a T if it precedes an F\r\n" );
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document.write( "Now I will cross out the list that I just used to\r\n" );
document.write( "get the list under the ~\r\n" );
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document.write( "Now there is only one symbol left to put a list under.\r\n" );
document.write( "It has the list TTTF on the left of it and FFTT on the\r\n" );
document.write( "right of it so we put the list FFTF under it, because \"^\" \r\n" );
document.write( "only gets a T in the third line because that's the only\r\n" );
document.write( "line that has T's on both sides.  The other three lines\r\n" );
document.write( "get T's\r\n" );
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document.write( "so we have this:\r\n" );
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document.write( "Finally we cross out the lines we just used\r\n" );
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document.write( "The answer is FFTF\r\n" );
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document.write( "Edwin
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