Solver Check to See if Two Sets Are Equal or Equinumerous

Source code of 'Check to See if Two Sets Are Equal or Equinumerous'

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==section input
This solver will determine if two sets are equal or <a href=http://en.wikipedia.org/wiki/Equinumerosity>equinumerous</a>.

Enter two sets in which each element is separated by a comma

A = {*[input 30 set1=a,b,c,d]} 
B = {*[input 30 set2=d,e,f]}

Now fill in the blank by choosing if you want to see if the two sets are equal or if the two sets are equinumerous:

I want to determine if the two sets are *[choice path equal equinumerous]

==section solution

perl

### Subroutines

## remove duplicates from an array
sub remove_duplicates {
my (@arr);
@arr=@_;

for(my $i=0;$i<@arr;$i++)
 {
 for(my $j=0;$j<@arr;$j++)
 {if($i!=$j)
 {if($arr[$i] eq $arr[$j])
 {splice(@arr,$i,1) if $i>$j;
 splice(@arr,$j,1) if $j>$i;
 }
 }
 }
 }

return @arr;
}

## checks to see if element is member of set
sub is_element_of
{
 my ($element,@set)=@_;
 for (my $i=0;$i<@set;$i++)
 {
 if($element eq $set[$i])
 {
 return 1;
 }
 }
 return 0;
}

## given two sets A and B, determine if A is a subset of B
sub is_subset_of
{
 die "Needs two arguments: Set A and Set B" if @_!=2;
 my ($set1,$set2)=@_;
 my @set1=remove_duplicates(split(/,/,$set1));
 my @set2=remove_duplicates(split(/,/,$set2));
 return 0 if @set1>@set2;
 my $count=0;
 for (my $i=0;$i<@set1;$i++)
 {
 $count++ if(is_element_of($set1[$i],@set2));
 }
 return 1 if $count==@set1;
 return 0;
}

## given two sets A and B, determine if A = B
sub is_equal
{
   die "Needs two arguments: Set A and Set B" if @_!=2;
   my ($set1,$set2)=@_;
   my @set1=remove_duplicates(split(/,/,$set1));
   my @set2=remove_duplicates(split(/,/,$set2));
   return 1 if( is_subset_of(join(",",@set1),join(",",@set2)) and is_subset_of(join(",",@set2),join(",",@set1)) );
   return 0;
}

### End Subroutines

$set1=~s/\s//g;
$set1=~s/^,//;
$set1=~s/,$//;
$set2=~s/\s//g;
$set2=~s/^,//;
$set2=~s/,$//;

### Error Checking
my $error_check1=$set1;
$error_check1=~s/\-|\/|\.|,//g;
if($error_check1=~m/\W/)
{
 print "Error: Invalid Symbol";
 goto end;
}

my $error_check2=$set2;
$error_check2=~s/\-|\/|\.|,//g;
if($error_check2=~m/\W/)
{
 print "Error: Invalid Symbol";
 goto end;
}

if($error_check1 eq '' or $error_check2 eq '')
{
 print "Error: One of the sets is empty. Please enter values.";
 goto end;
}

### End Error Checking

my @set1=split(/,/,$set1);
my @set2=split(/,/,$set2);

if($path eq 'equal')
{

print " To determine if <a href=http://en.wikipedia.org/wiki/Set_%28mathematics%29>set</a> *[Tex \\LARGE A=\\left\\{$set1\\right\\}] is equal to set *[Tex \\LARGE B=\\left\\{$set2\\right\\}], we need to check two things: ";

print " 1) Is EVERY element of A also an element of B? In other words, is A a <a href=http://en.wikipedia.org/wiki/Subset>subset</a> of B? ";
 print " 2) Is EVERY element of B also an element of A? In other words, is B a <a href=http://en.wikipedia.org/wiki/Subset>subset</a> of A? ";

print " If the answer to BOTH of these questions are \"yes\", then this will mean that *[Tex \\LARGE A=B]. Otherwise, *[Tex \\LARGE A \\neq B]. ";

print " So let's answer the questions above: ";

print " 1) ";

my $ans=0;  #0 - false (not equal) 1 - true (equal)

## if A is NOT a subset of B....
 if( !is_subset_of( join(",",@set1) , join(",",@set2) ) )
 {
 print "Since A is NOT a subset of B (check out <a href=http://www.algebra.com/algebra/homework/Subset/subset-test.solver>this solver</a> to do a subset test), this means that *[Tex \\LARGE A \\neq B]. ";
 goto end1;

}
 else
 {
 print "In this case, A is a subset of B (check out <a href=http://www.algebra.com/algebra/homework/Subset/subset-test.solver>this solver</a> to do a subset test). So let's move onto the next question. ";
 }

print " 2) ";

## if B is NOT a subset of A....
 if( !is_subset_of( join(",",@set2) , join(",",@set1) ) )
 {
 print "Since B is NOT a subset of A (check out <a href=http://www.algebra.com/algebra/homework/Subset/subset-test.solver>this solver</a> to do a subset test), this means that *[Tex \\LARGE A \\neq B]. ";

}
 else
 {
 print "In this case, B is a subset of A (check out <a href=http://www.algebra.com/algebra/homework/Subset/subset-test.solver>this solver</a> to do a subset test). Since A is a subset of B AND B is a subset of A, this means *[Tex \\LARGE A=B]. ";
 $ans=1;
 }

end1:

print " So the two sets *[Tex \\LARGE A=\\left\\{$set1\\right\\}] and *[Tex \\LARGE B=\\left\\{$set2\\right\\}] are equal." if $ans==1;

print " So the two sets *[Tex \\LARGE A=\\left\\{$set1\\right\\}] and *[Tex \\LARGE B=\\left\\{$set2\\right\\}] are NOT equal." if $ans==0;
}

if($path eq 'equinumerous')
{

print "Recall that two sets are <a href=http://en.wikipedia.org/wiki/Equinumerosity>equinumerous</a> if they have the same number of elements. Those elements can be different, but as long as the number of elements are the same, then the two sets are are <a href=http://en.wikipedia.org/wiki/Equinumerosity>equinumerous</a>. ";

print " In this case, there are ".@set1." element";
print "s" if @set1>1;
print " in the set *[Tex \\LARGE A=\\left\\{$set1\\right\\}] and ".@set2." element";
print "s" if @set2>1;
print " in the set *[Tex \\LARGE B=\\left\\{$set2\\right\\}]. ";

if(@set1!=@set2)
{
 print " Since the number of elements in set A (which is ".@set1.") is NOT equal to the number of elements in set B (which is ".@set2."), this means that the two sets A and B are NOT equinumerous. ";
}
else
{
 print " Since the number of elements in set A (which is ".@set1.") is equal to the number of elements in set B (which is ".@set2."), this means that the two sets A and B are equinumerous. In other words, there's a one-to-one correspondence between the elements in sets A and B. ";
}

}

end:

==section output

==section check