document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188729>Question 1188729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is the argument invalid or valid?\r<BR>\n" );
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document.write( "1. R ⊃ (K • U)       <BR>\n" );
document.write( "2. A ⊃ (Q • R)<BR>\n" );
document.write( "3. S • A        ∴ U </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819891 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "An argument is invalid if we have all true premises that lead to a false conclusion. Otherwise, we consider it valid.\r<BR>\n" );
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document.write( "If premise 3 was true, then both statements S and A must be true. Otherwise S * A is false. The * or dot symbol means \"and\" in terms of logic. Refer to \"conjunction\".\r<BR>\n" );
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document.write( "Since A is true, this means Q*R must be true. Recall that stuff of the form P -> Q is false when P = True and Q = false. Otherwise, P -> Q is true. The fact that statement A is true means we might have premise 2 to be false if Q*R were false. So that's why we need Q*R to be true.\r<BR>\n" );
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document.write( "If Q*R is true, then so are the individual components Q and R.\r<BR>\n" );
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document.write( "Use this line of logic to see that R being true leads to K and U being true as well (premise 1).\r<BR>\n" );
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document.write( "As you can see, all three premises are true and they lead to a true conclusion (statement U). \r<BR>\n" );
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document.write( "Therefore, this argument is valid.<BR>\n" );
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