document.write( "Question 452592: Construct a truth table for (~p⋁q) ↔ p \n" ); document.write( "
Algebra.Com's Answer #311108 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Start out putting TTFF under the p's and TFTF under the q\r\n" );
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document.write( "(~p ⋁ q) ↔ p\r\n" );
document.write( "  T   T    T  \r\n" );
document.write( "  T   F    T\r\n" );
document.write( "  F   T    F\r\n" );
document.write( "  F   F    F\r\n" );
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document.write( "Then under the ~ put the negation (opposite) of what's \r\n" );
document.write( "under the p.  That is FFTT and scratch what's under \r\n" );
document.write( "the p:\r\n" );
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document.write( "(~p ⋁ q) ↔ p\r\n" );
document.write( " FT   T    T  \r\n" );
document.write( " FT   F    T\r\n" );
document.write( " TF   T    F\r\n" );
document.write( " TF   F    F\r\n" );
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document.write( "Then under the ⋁ put F if there are F's on both sides of\r\n" );
document.write( "it and T the other times, then scratch through the columns on \r\n" );
document.write( "the sides of it.  That is, TFTT.\r\n" );
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document.write( "(~p ⋁ q) ↔ p\r\n" );
document.write( " FT T T    T  \r\n" );
document.write( " FT F F    T\r\n" );
document.write( " TF T T    F\r\n" );
document.write( " TF T F    F\r\n" );
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document.write( "Then finally under the ↔ put the T if it has the same \r\n" );
document.write( "thing on the left of it that it has on the right of it, and F\r\n" );
document.write( "otherwise.  That is, put TFFF, and scratch through what's\r\n" );
document.write( "on both sides of it:\r\n" );
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document.write( "(~p ⋁ q) ↔ p\r\n" );
document.write( " FT T T  T T  \r\n" );
document.write( " FT F F  F T\r\n" );
document.write( " TF T T  F F\r\n" );
document.write( " TF F F  F F\r\n" );
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document.write( "The answer is TFFF which is also the\r\n" );
document.write( "truth table for p⋀q, so the above\r\n" );
document.write( "expression is equivalent to p⋀q.\r\n" );
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document.write( "Edwin
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