# Initialization

DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "PGchoicemacros.pl",
  "MathObjects.pl",
  "answerHints.pl",
  "PGcourse.pl",
  "contextSetOfSets.pl",
  "PGML.pl",
  "setshelp.pl",
);

TEXT(beginproblem());


# Variables

Context("SetOfSets");

@slice = NchooseK(12,9);
@A = ($slice[1], $slice[2], $slice[3], $slice[4], $slice[5]);
@B = ($slice[1], $slice[2], $slice[3], $slice[6]);
@AiB = ($slice[1], $slice[2], $slice[3]);
@AuB = ($slice[1], $slice[2], $slice[3], $slice[4], $slice[5], $slice[6]);

for ($k=4; $k>0; $k-=1) {
  for ($i=0; $i<$k; $i+=1){
    if($A[$i]>$A[$k]) {
       $b = $A[$i];
       $A[$i] = $A[$k];
       $A[$k] = $b;
    }
  }
}

for ($k=3; $k>0; $k-=1) {
  for ($i=0; $i<$k; $i+=1){
    if($B[$i]>$B[$k]) {
       $b = $B[$i];
       $B[$i] = $B[$k];
       $B[$k] = $b;
    }
  }
}

@AuB = ();
@AiB = ();
$num = random(7,16);

$caseeo = random(1,2);
@words = ("even", "odd");
$word = $words[$caseeo%2];

$dispA = "A = \{ $A[0], $A[1], $A[2], $A[3], $A[4] \}";
$dispB = "B = \{ x \mid x \mbox{ is an $word positive integer less than } $num \}";
$count = 0;
for ($i = 0+$caseeo; $i < $num; $i=$i+2) {
  for ($j = 0; $j < scalar(@A); $j++) {
    if ($A[$j] == $i) {
      push(@AiB,$i);
    }
    $eos[$count] = $i;
    $count++;
  }
}
$ans_a = Set(@AiB);
@AuB = (@eos,@A);
$ans_b = Set(@AuB);

if (scalar @AiB == 0) {
  $ans_a = Compute("{}");
}


# Main problem

BEGIN_PGML

Let [` [@ $dispA @]* `] and [` [@ $dispB @]* `].

Determine the following sets. Express your answers using [@ htmlLink("#","set notation","onClick='openhelpCustom1()';") @]*.

[` A \cap B `] = [_____________________]{$ans_a}

[` A \cup B `] = [_____________________]{$ans_b}

END_PGML


# Answer evaluation

$showPartialCorrectAnswers = 0;


ENDDOCUMENT();