document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485685>Question 485685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help again, i have also posted this problem several times, and yet no response.<BR>\n" );
document.write( "determine which if any of the three statements are equivalent. give a reason for your conclusion, and show complete work.<BR>\n" );
document.write( "i)if the dog wags its tail, then the dog is not calm.<BR>\n" );
document.write( "ii)either the dog does not wag its tail or the dog is not calm<BR>\n" );
document.write( "iii) if the dog is not calm, then the dog wags its tail.\r<BR>\n" );
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document.write( "thank you for your help.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332157 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i)if the dog wags its tail, then the dog is not calm.<BR>\n" );
document.write( "ii)either the dog does not wag its tail or the dog is not calm<BR>\n" );
document.write( "iii) if the dog is not calm, then the dog wags its tail.\r<BR>\n" );
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document.write( "p = the dog wags its tail.<BR>\n" );
document.write( "q = the dog is not calm.\r<BR>\n" );
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document.write( "~p = the dog does not wag its tail.<BR>\n" );
document.write( "~q = the dog is calm.\r<BR>\n" );
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document.write( "statement 1 translates to p -> q<BR>\n" );
document.write( "statement 2 translates to ~p v q<BR>\n" );
document.write( "statement 3 translates to q -> p\r<BR>\n" );
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document.write( "statement 1 and 3 are not equivalent<BR>\n" );
document.write( "we need to test with statement 2 to see if it's equivalent to either one of the other 2.\r<BR>\n" );
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document.write( "when in doubt, you need to do a truth table.<BR>\n" );
document.write( "it tells you whether the statement are equivalent or not.\r<BR>\n" );
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document.write( "the truth table for these 3 statements is shown in the following picture.\r<BR>\n" );
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document.write( "in this table:\r<BR>\n" );
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document.write( "statement 1 becomes statement A.<BR>\n" );
document.write( "statement 2 becomes statement B.<BR>\n" );
document.write( "statement 3 becomes statement C.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/problems/truth_table_1.jpg\" alt = \"$$$$$\"/ >\r<BR>\n" );
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document.write( "The truth table says that (p -> q) is equivalent to (~q v p).\r<BR>\n" );
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document.write( "That means that statement 1 is equivalent to statement 2.\r<BR>\n" );
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document.write( "It would be difficult to see this without use of the truth table.\r<BR>\n" );
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document.write( "Logically, trying to make sense of it takes a little stretch.\r<BR>\n" );
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document.write( "I believe the answer lies in the law of disjunction.\r<BR>\n" );
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document.write( "The law of disjunction states:\r<BR>\n" );
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document.write( "if A or B is true, then:<BR>\n" );
document.write( "If A is false, then B must be true.<BR>\n" );
document.write( "If B is false, than A must be true.\r<BR>\n" );
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document.write( "we have 2 statements that we think are equivalent because the truth table test of equivalency says that they are.\r<BR>\n" );
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document.write( "The 2 statements are:\r<BR>\n" );
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document.write( "i)if the dog wags its tail, then the dog is not calm.<BR>\n" );
document.write( "ii)either the dog does not wag its tail or the dog is not calm\r<BR>\n" );
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document.write( "the contra-positive of the first statement and the first statement are equivalent.\r<BR>\n" );
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document.write( "The first statement is:<BR>\n" );
document.write( "if the dog wags its tail, then the dog is not calm.<BR>\n" );
document.write( "The contra-positive to the first statement is:<BR>\n" );
document.write( "if the dog is calm, then the dog does not wag its tail.\r<BR>\n" );
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document.write( "The second statement is:<BR>\n" );
document.write( "either the dog does not wag its tail or the dog is not calm.\r<BR>\n" );
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document.write( "If we assume that the dog does not wag its tail is false, then the law of disjunction says that the dog is not calm must be true.\r<BR>\n" );
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document.write( "we can write this another way to say:<BR>\n" );
document.write( "if the dog wags its tail, then the dog is not calm.<BR>\n" );
document.write( "that looks very much like the first statement.\r<BR>\n" );
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document.write( "if we assume that the dog is not calm is false, then the dog does not wag its tail must be true by the same law of disjunction.\r<BR>\n" );
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document.write( "we can write this another way to say:<BR>\n" );
document.write( "if the dog is calm, then the dog does not wag its tail.<BR>\n" );
document.write( "that looks very much like the contra-positive to the first statement.\r<BR>\n" );
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document.write( "i'm satisfied that the truth table is telling the truth and that statements 1 and 2 are equivalent even though anybody would be hard pressed to determine that they are without using the rules of logic to confirm that.\r<BR>\n" );
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document.write( "the truth table test is the way to determine the equivalency of two statements.\r<BR>\n" );
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document.write( "that's called demorgan's law i believe.\r<BR>\n" );
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document.write( "here's some additional reading for you if i didn't send it to you earlier.<BR>\n" );
document.write( "there are references in there as well so you can study to your heart's content if you so desire.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.algebra.com/algebra/homework/Conjunction/THEO-061210.lesson\" target = \"_blank\">STATEMENT LAWS AND FALLACIES</a>\r<BR>\n" );
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