View of /trunk/rochester_problib/instructiveProblems/OldProblems/Sets_2.pg

    1 ##DESCRIPTION
    2 # Name of the file: Sets_2.pg
    3 # File Created: 6/29/05
    4 # Problem Author: Modified by Shafiu Jibrin
    5 #                 from setSets/ur_st_1_2.pg
    6 
    7 # Location: Northern Arizona University
    8 # Course:
    9 # Recommended trials:
   10 # Recommended value:
   11 #
   12 ##ENDDESCRIPTION
   13 
   14 ##KEYWORDS('Sets')
   15 
   16 DOCUMENT();        # This should be the first executable line in the problem.
   17 
   18 loadMacros(
   19 "PGasu.pl",
   20 "PG.pl",
   21 "PGbasicmacros.pl",
   22 "PGchoicemacros.pl",
   23 "PGanswermacros.pl",
   24 "PGgraphmacros.pl",
   25 "extraAnswerEvaluators.pl",
   26 "PGcourse.pl",
   27 # "source.pl",
   28 );
   29 
   30 TEXT(&beginproblem);
   31 $showPartialCorrectAnswers = 1;
   32 
   33 ###################
   34 #
   35 #  Setup
   36 
   37 @slice = NchooseK(12,9);
   38 @A = ($slice[1], $slice[2], $slice[3], $slice[4], $slice[5]);
   39 @B = ($slice[1], $slice[2], $slice[3], $slice[6]);
   40 @C = ($slice[1], $slice[4], $slice[6], $slice[7], $slice[8], $slice[0]);
   41 @AiB = ($slice[1], $slice[2], $slice[3]);
   42 @AuB = ($slice[1], $slice[2], $slice[3], $slice[4], $slice[5], $slice[6]);
   43 @BUCiA = ($slice[1], $slice[2], $slice[3], $slice[4]);
   44 @BuCIA = ($slice[1], $slice[2], $slice[3], $slice[4], $slice[6]);
   45 
   46 for ($k=4; $k>0; $k-=1) {
   47   for ($i=0; $i<$k; $i+=1){
   48     if($A[$i]>$A[$k]) {
   49        $b = $A[$i];
   50        $A[$i] = $A[$k];
   51        $A[$k] = $b;
   52     }
   53   }
   54 }
   55 
   56 for ($k=3; $k>0; $k-=1) {
   57   for ($i=0; $i<$k; $i+=1){
   58     if($B[$i]>$B[$k]) {
   59        $b = $B[$i];
   60        $B[$i] = $B[$k];
   61        $B[$k] = $b;
   62     }
   63   }
   64 }
   65 
   66 for ($k=5; $k>0; $k-=1) {
   67   for ($i=0; $i<$k; $i+=1){
   68     if($C[$i]>$C[$k]) {
   69        $b = $C[$i];
   70        $C[$i] = $C[$k];
   71        $C[$k] = $b;
   72     }
   73   }
   74 }
   75 
   76 for ($k=2; $k>0; $k-=1) {
   77   for ($i=0; $i<$k; $i+=1){
   78     if($AiB[$i]>$AiB[$k]) {
   79        $b = $AiB[$i];
   80        $AiB[$i] = $AiB[$k];
   81        $AiB[$k] = $b;
   82     }
   83   }
   84 }
   85 
   86 for ($k=5; $k>0; $k-=1) {
   87   for ($i=0; $i<$k; $i+=1){
   88     if($AuB[$i]>$AuB[$k]) {
   89        $b = $AuB[$i];
   90        $AuB[$i] = $AuB[$k];
   91        $AuB[$k] = $b;
   92     }
   93   }
   94 }
   95 
   96 for ($k=3; $k>0; $k-=1) {
   97   for ($i=0; $i<$k; $i+=1){
   98     if($BUCiA[$i]>$BUCiA[$k]) {
   99        $b = $BUCiA[$i];
  100        $BUCiA[$i] = $BUCiA[$k];
  101        $BUCiA[$k] = $b;
  102     }
  103   }
  104 }
  105 
  106 for ($k=4; $k>0; $k-=1) {
  107   for ($i=0; $i<$k; $i+=1){
  108     if($BuCIA[$i]>$BuCIA[$k]) {
  109        $b = $BuCIA[$i];
  110        $BuCIA[$i] = $BuCIA[$k];
  111        $BuCIA[$k] = $b;
  112     }
  113   }
  114 }
  115 
  116 $LEFT_BRACE = '\{';
  117 $RIGHT_BRACE = '\}';
  118 
  119 ###################
  120 #
  121 #  Text
  122 
  123 BEGIN_TEXT
  124 
  125 Let \( A= ${LEFT_BRACE} $A[0],  $A[1], $A[2], $A[3],  $A[4] ${RIGHT_BRACE}\) , $SPACE
  126 \( B= ${LEFT_BRACE} $B[0],  $B[1],  $B[2],  $B[3]  ${RIGHT_BRACE}\) , $SPACE
  127 \( C= ${LEFT_BRACE} $C[0],  $C[1],  $C[2], $C[3], $C[4], $C[5] ${RIGHT_BRACE}\). $BR
  128 List the elements of the following sets. If there is more than one element
  129 write them separated by commas. $BR
  130 
  131 \( A \cap B = ${LEFT_BRACE} \) \{ans_rule(25)\}
  132 \(${RIGHT_BRACE}\) $BR
  133 
  134 \( A \cup B = ${LEFT_BRACE} \) \{ans_rule(25)\} \(${RIGHT_BRACE}\) $BR
  135 
  136 \( (B \cup C) \cap A = ${LEFT_BRACE} \) \{ans_rule(25)\} \(${RIGHT_BRACE}\) $BR
  137 
  138 END_TEXT
  139 
  140 ###################
  141 #
  142 #  Answers
  143 
  144 &ANS(number_list_cmp("$AiB[0],$AiB[1],$AiB[2]"));
  145 
  146 &ANS(number_list_cmp("$AuB[0],$AuB[1],$AuB[2],$AuB[3],$AuB[4],$AuB[5]"));
  147 
  148 &ANS(number_list_cmp("$BUCiA[0],$BUCiA[1],$BUCiA[2],$BUCiA[3]"));
  149 
  150 ENDDOCUMENT();       # This should be the last executable line in the problem.