document.write( "Question 1184203: Construct a truth table to determine if the given proposition is a tautology or not:\r
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Algebra.Com's Answer #814784 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( " The rule for ~ is \"If a T follows it, the result is F, and\r\n" );
document.write( "                   if an F follows it, the result if T.\"\r\n" );
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document.write( " The rule for v is \"If there is a T on either side of it, the result is T\"\r\n" );
document.write( "                    It is only F if there are F's on both sides.\r\n" );
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document.write( " The rule for ^ is \"If there is an F on either side of it, the result is F\"\r\n" );
document.write( "                    It is only T if there are T's on both sides.\r\n" );
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document.write( " The rule for -> is \"If it has T on the left and F on the right, the result\r\n" );
document.write( "                    is F.  Otherwise the result is T\"\r\n" );
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document.write( " The rule for <-> is \"If it has the same on both sides, the result is T\".\r\n" );
document.write( "                     If it has T's on both sides, the result is T.\r\n" );
document.write( "                     If it has F's on both sides, the result is T.\r\n" );
document.write( "                     If it has T on one side and F on the other side, the\r\n" );
document.write( "                     result is F.\r\n" );
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document.write( " Put TTFF under A, and TFTF under B, and follow the above rules:\r\n" );
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document.write( "  A | B | ~A |~B | Av~B | ~(Av~B) | ~A^B || ~(Av~B)<->(~A^B)\r\n" );
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document.write( "  T | T |  F | F |  T   |     F   |   F  ||         T\r\n" );
document.write( "  T | F |  F | T |  T   |     F   |   F  ||         T\r\n" );
document.write( "  F | T |  T | F |  F   |     T   |   T  ||         T\r\n" );
document.write( "  F | F |  T | T |  T   |     F   |   F  ||         T\r\n" );
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document.write( " Since the truth table came out with all T's on the right end, the\r\n" );
document.write( " proposition is a tautology.\r\n" );
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document.write( " Edwin

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