document.write( "Question 1164740: Explain, without using a truth table, while the statement (p ∨ ¬q) ∧ (q ∨ ¬r) ∧ (r → ¬p)
\n" );
document.write( "is true when at least one of p,q,r is true, and at least one is false, and why the statement is false when p, q, r all have the same truth value. \n" );
document.write( "
Algebra.Com's Answer #789161 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "Something is wrong with the wording here, because the words:\r\n" ); document.write( "\"true when at least one of p,q,r is true\" \r\n" ); document.write( "contradict the words:\r\n" ); document.write( "\"false when p, q, r all have the same truth value.\" \r\n" ); document.write( "whenever p, q, r are all TRUE.\r\n" ); document.write( "\r\n" ); document.write( "That's because when p, q, r are all true, then certainly at least one is\r\n" ); document.write( "true, so the statement is TRUE.\r\n" ); document.write( "However, also when p, q, r are all true, then they all have the same truth\r\n" ); document.write( "value, so the statement is FALSE.\r\n" ); document.write( "\r\n" ); document.write( "The statement can't be both TRUE and FALSE, so you need to ask your teacher\r\n" ); document.write( "to correct the wording.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |