document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188838>Question 188838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I saw that people can solve logic proofs on this site. I've looked everywhere for help. Could I get help with these two?\r<BR>\n" );
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document.write( "1. p v (q & r)<BR>\n" );
document.write( "2. ~r<BR>\n" );
document.write( "3. p -> (s -> ~t)   /:. (therefore) ~(s & t)\r<BR>\n" );
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document.write( "AND\r<BR>\n" );
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document.write( "1. (p <--> q) -> s<BR>\n" );
document.write( "2. ~(~r -> t)<BR>\n" );
document.write( "3. ~q v ~s         /:. (t v p) -> (~t & ~q)\r<BR>\n" );
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document.write( "I would write what I have so far but I know that it's really wrong and it just confused me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141630 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</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=141630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. p v (q & r)<BR>\n" );
document.write( "2. ~r<BR>\n" );
document.write( "3. p -> (s -> ~t) <BR>\n" );
document.write( ":. (therefore) ~(s & t) \r<BR>\n" );
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document.write( "Write the conjunction of premises 1 and 2:\r<BR>\n" );
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document.write( "       [p v (q & r)] & ~r \r<BR>\n" );
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document.write( "Distribute inside the bracket:\r<BR>\n" );
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document.write( "      [(p v q) & (p v r)] & ~r\r<BR>\n" );
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document.write( "Use the associative law to move the bracket:\r<BR>\n" );
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document.write( "      (p v q) & [(p v r) & ~r]\r<BR>\n" );
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document.write( "Use the associative law inside the bracket <BR>\n" );
document.write( "to move the parentheses:\r<BR>\n" );
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document.write( "      (p v q) & [(p v (r & ~r)]\r<BR>\n" );
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document.write( "(r & ~r) is a contradiction so we replace it by F\r<BR>\n" );
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document.write( "      (p v q) & [p v F]\r<BR>\n" );
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document.write( "Us the distributive law in revers to \"factor\" out \" p v \"\r<BR>\n" );
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document.write( "      p v (q v F)\r<BR>\n" );
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document.write( "F is the identity for v so we can replace p by p v F\r<BR>\n" );
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document.write( "      (p v q) & (p v F)\r<BR>\n" );
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document.write( "Use the distributive law to factor out \" p v \"\r<BR>\n" );
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document.write( "      p v (q & F)\r<BR>\n" );
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document.write( "Since F is the annihilator for & we can replace (q & F) by F\r<BR>\n" );
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document.write( "      p v F\r<BR>\n" );
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document.write( "Since F is the identity for v we can replace that by p\r<BR>\n" );
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document.write( "       p\r<BR>\n" );
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document.write( "Now we take the conjunction of this with premise 3.\r<BR>\n" );
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document.write( "       p & [p -> (s -> ~t)]\r<BR>\n" );
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document.write( "Since x -> y is equivalent to ~x v y, we<BR>\n" );
document.write( "can write the bracket thusly:\r<BR>\n" );
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document.write( "       p & [~p v (s -> ~t)]\r<BR>\n" );
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document.write( "Use the distributive law:\r<BR>\n" );
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document.write( "      (p & ~p) v [p & (s -> ~t)]\r<BR>\n" );
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document.write( "(p & ~p) is a contradiction so we can replace it by F\r<BR>\n" );
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document.write( "             F v [p & (s -> ~t)]              \r<BR>\n" );
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document.write( "Since F is the identity for v, we can eliminate the F v\r<BR>\n" );
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document.write( "                  p & (s -> ~t)\r<BR>\n" );
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document.write( "Use the fact that x & y -> y, so we can eliminate \" p & \"\r<BR>\n" );
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document.write( "                       s -> ~t\r<BR>\n" );
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document.write( "Since x -> y is equivalent to ~x v y, we<BR>\n" );
document.write( "can write that as<BR>\n" );
document.write( "                       ~s v ~t\r<BR>\n" );
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document.write( "We can use DeMorgan's law to \"factor\" out ~ and get\r<BR>\n" );
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document.write( "                      ~(s & t)\r<BR>\n" );
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document.write( "     </SPAN>\n" );
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