document.write( "Question 588008: In need of help!!!!\r
\n" ); document.write( "\n" ); document.write( "Use truth tables to test the validity of the argument.\r
\n" ); document.write( "\n" ); document.write( "p → ~q
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\n" ); document.write( "∴ p ∨ q \n" ); document.write( "
Algebra.Com's Answer #374347 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since a truth table would be so long, and you'd have to have a very wide\r\n" );
document.write( "piece of paper to get it all in, I'd just take the four cases and work each\r\n" );
document.write( "one out separately and see if we get T in every case:\r\n" );
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document.write( "Case p=T and q=T\r\n" );
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document.write( "[(p -> ~q) ^ (q -> ~p)] -> (p V q)\r\n" );
document.write( "[(T -> ~T) ^ (T -> ~T)] -> (T V T)\r\n" );
document.write( "[(T -> F ) ^ (T ->  F)] ->    T\r\n" );
document.write( "[    F     ^     F    ] ->    T\r\n" );
document.write( "           F            ->    T\r\n" );
document.write( "                         T\r\n" );
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document.write( "Case p=T and q=F\r\n" );
document.write( "[(p -> ~q) ^ (q -> ~p)] -> (p V q)\r\n" );
document.write( "[(T -> ~F) ^ (F -> ~T)] -> (T V F)\r\n" );
document.write( "[(T -> T ) ^ (F -> F) ] ->    T\r\n" );
document.write( "[    T     ^     T    ] ->    T\r\n" );
document.write( "           T            ->    T\r\n" );
document.write( "                         T\r\n" );
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document.write( "Case p=F and q=T\r\n" );
document.write( "[(p -> ~q) ^ (q -> ~p)] -> (p V q)\r\n" );
document.write( "[(F -> ~T) ^ (T -> ~F)] -> (F V T)\r\n" );
document.write( "[(F -> F ) ^ (T -> F )] ->    T\r\n" );
document.write( "[    T     ^     F    ] ->    F\r\n" );
document.write( "           F            ->    F\r\n" );
document.write( "                         T\r\n" );
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document.write( "Case p=F and q=F\r\n" );
document.write( "[(p -> ~q) ^ (q -> ~p)] -> (p V q)\r\n" );
document.write( "[(F -> ~F) ^ (F -> ~F)] -> (F V F)\r\n" );
document.write( "[(F -> T ) ^ (F -> T )] ->    F\r\n" );
document.write( "[    T     ^     F    ] ->    F\r\n" );
document.write( "           F            ->    F\r\n" );
document.write( "                         T\r\n" );
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document.write( "All four cases come out T, so the argument is valid.\r\n" );
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document.write( "Edwin
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