document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927200>Question 927200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use ordinary truth tables to answer the following problem. <BR>\n" );
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document.write( "Given the argument: B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B, this argument is:<BR>\n" );
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document.write( "Invalid; fails in 3rd line.<BR>\n" );
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document.write( "Invalid; fails in 2nd line.<BR>\n" );
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document.write( "Invalid; fails in 1st line.<BR>\n" );
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document.write( "Invalid; fails in 4th line.<BR>\n" );
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document.write( "Valid.\r<BR>\n" );
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document.write( "I have tried to break up the question and use the T & F in the lines but keep messing up on my placement. Can someone help me so that I can understand what I am doing wrong. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562827 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "I use the method of truth tables where you begin\r\n" );
document.write( "with T's and F's under only the letters, and end up \r\n" );
document.write( "with T's and F's under only the symbols.\r\n" );
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document.write( "Put TTTTFFFF under B\r\n" );
document.write( "Put TTFFTTFF under M\r\n" );
document.write( "Put TFTFTFTF under K\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "T   T   T      T     T      T    T \r\n" );
document.write( "T   T   T      F     F      T    T\r\n" );
document.write( "T   F   T      T     T      F    T\r\n" );
document.write( "T   F   T      F     F      F    T\r\n" );
document.write( "F   T   F      T     T      T    F\r\n" );
document.write( "F   T   F      F     F      T    F\r\n" );
document.write( "F   F   F      T     T      F    F\r\n" );
document.write( "F   F   F      F     F      F    F\r\n" );
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document.write( "Do B &#8744; M, which is T unless both sides false.\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
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document.write( "T T T   T      T     T      T    T \r\n" );
document.write( "T T T   T      F     F      T    T\r\n" );
document.write( "T T F   T      T     T      F    T\r\n" );
document.write( "T T F   T      F     F      F    T\r\n" );
document.write( "F T T   F      T     T      T    F\r\n" );
document.write( "F T T   F      F     F      T    F\r\n" );
document.write( "F F F   F      T     T      F    F\r\n" );
document.write( "F F F   F      F     F      F    F\r\n" );
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document.write( "Now erase the columns under the first B and M columns:\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T     T      T     T      T    T \r\n" );
document.write( "  T     T      F     F      T    T\r\n" );
document.write( "  T     T      T     T      F    T\r\n" );
document.write( "  T     T      F     F      F    T\r\n" );
document.write( "  T     F      T     T      T    F\r\n" );
document.write( "  T     F      F     F      T    F\r\n" );
document.write( "  F     F      T     T      F    F\r\n" );
document.write( "  F     F      F     F      F    F\r\n" );
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document.write( "Now just left of the first K column, do ~ K \r\n" );
document.write( "by putting the opposite of what's under K under ~.\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T     T    F T     T      T    T \r\n" );
document.write( "  T     T    T F     F      T    T\r\n" );
document.write( "  T     T    F T     T      F    T\r\n" );
document.write( "  T     T    T F     F      F    T\r\n" );
document.write( "  T     F    F T     T      T    F\r\n" );
document.write( "  T     F    T F     F      T    F\r\n" );
document.write( "  F     F    F T     T      F    F\r\n" );
document.write( "  F     F    T F     F      F    F\r\n" );
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document.write( "Erase the column under K\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T     T    F       T      T    T \r\n" );
document.write( "  T     T    T       F      T    T\r\n" );
document.write( "  T     T    F       T      F    T\r\n" );
document.write( "  T     T    T       F      F    T\r\n" );
document.write( "  T     F    F       T      T    F\r\n" );
document.write( "  T     F    T       F      T    F\r\n" );
document.write( "  F     F    F       T      F    F\r\n" );
document.write( "  F     F    T       F      F    F\r\n" );
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document.write( "Do B &#8744; &#8764; K, which is T unless both sides false.\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T     T T  F       T      T    T \r\n" );
document.write( "  T     T T  T       F      T    T\r\n" );
document.write( "  T     T T  F       T      F    T\r\n" );
document.write( "  T     T T  T       F      F    T\r\n" );
document.write( "  T     F F  F       T      T    F\r\n" );
document.write( "  T     F T  T       F      T    F\r\n" );
document.write( "  F     F F  F       T      F    F\r\n" );
document.write( "  F     F T  T       F      F    F\r\n" );
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document.write( "Erase the columns we just used to put a\r\n" );
document.write( "column under the &#8744;\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T       T          T      T    T \r\n" );
document.write( "  T       T          F      T    T\r\n" );
document.write( "  T       T          T      F    T\r\n" );
document.write( "  T       T          F      F    T\r\n" );
document.write( "  T       F          T      T    F\r\n" );
document.write( "  T       T          F      T    F\r\n" );
document.write( "  F       F          T      F    F\r\n" );
document.write( "  F       T          F      F    F\r\n" );
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document.write( "Now just left of the second M column, do ~ M \r\n" );
document.write( "by putting the opposite of what's under M under ~.\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T       T          T    F T    T \r\n" );
document.write( "  T       T          F    F T    T\r\n" );
document.write( "  T       T          T    T F    T\r\n" );
document.write( "  T       T          F    T F    T\r\n" );
document.write( "  T       F          T    F T    F\r\n" );
document.write( "  T       T          F    F T    F\r\n" );
document.write( "  F       F          T    T F    F\r\n" );
document.write( "  F       T          F    T F    F\r\n" );
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document.write( "Erase the column under the second M\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T       T          T    F      T \r\n" );
document.write( "  T       T          F    F      T\r\n" );
document.write( "  T       T          T    T      T\r\n" );
document.write( "  T       T          F    T      T\r\n" );
document.write( "  T       F          T    F      F\r\n" );
document.write( "  T       T          F    F      F\r\n" );
document.write( "  F       F          T    T      F\r\n" );
document.write( "  F       T          F    T      F\r\n" );
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document.write( "Do K &#8744; ~ M, which is T unless both sides false.\r\n" );
document.write( "Blace result under the &#8744;.\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T       T          T T  F      T \r\n" );
document.write( "  T       T          F F  F      T\r\n" );
document.write( "  T       T          T T  T      T\r\n" );
document.write( "  T       T          F T  T      T\r\n" );
document.write( "  T       F          T T  F      F\r\n" );
document.write( "  T       T          F F  F      F\r\n" );
document.write( "  F       F          T T  T      F\r\n" );
document.write( "  F       T          F T  T      F\r\n" );
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document.write( "Now erase the columns under the first K and ~ columns:\r\n" );
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document.write( "B &#8744; M / B &#8744; &#8764; K // (K &#8744; &#8764; M) &#8835; B\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "  T       T            T         T \r\n" );
document.write( "  T       T            F         T\r\n" );
document.write( "  T       T            T         T\r\n" );
document.write( "  T       T            T         T\r\n" );
document.write( "  T       F            T         F\r\n" );
document.write( "  T       T            F         F\r\n" );
document.write( "  F       F            T         F\r\n" );
document.write( "  F       T            T         F\r\n" );
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document.write( "Since I am not sure what / and // mean, I\r\n" );
document.write( "can go no further. I do know what &#8835; means\r\n" );
document.write( "but I can't go any further until I learn \r\n" );
document.write( "what / and // stand for.  If you'll tell\r\n" );
document.write( "me what they stand for (conjunction?)\r\n" );
document.write( "(biconditional?) in the thank-you note\r\n" );
document.write( "below I'll be glad to finish.  \r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );