Solver Determine if Set A is a Subset of Set B

Source code of 'Determine if Set A is a Subset of Set B'

This Solver (Determine if Set A is a Subset of Set B) was created by by jim_thompson5910(35256)

: View Source, Show, Put on YOUR site
About jim_thompson5910: If you need more math help, then you can email me. I charge $2 for steps, or $1 for answers only. Email: jim_thompson5910@hotmail.com Website: http://www.freewebs.com/jimthompson5910/home.html

==section input
This solver will guide you through the process of determining if set A is a <a href=http://en.wikipedia.org/wiki/Subset>subset</a> of set B.

Enter two sets in which each element is separated by a comma (make sure that set A is smaller than set B; otherwise, you'll quickly find out that that A can't be a subset of B)

A = {*[input 30 set1=1,2,3]}
B = {*[input 30 set2=5,8,7,1,9,2,4,3]}

==section solution

perl

### Subroutines

##num_ordinate example: 1st, 2nd, 3rd

sub num_ordinate {
my ($number, $suffix);
$number=abs(shift);

if($number=~m/1$/)
 {$suffix="st";}
elsif($number=~m/2$/)
 {$suffix="nd";}
elsif($number=~m/3$/)
 {$suffix="rd";}
else
 {$suffix="th";}

$number.="$suffix" ;

return $number;}

## 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 an element, it returns the index of that element in the set (if that element is in there) or returns -1 if it's not in the set.
sub return_index
{
   my ($element,@set)=@_;
   return -1 unless is_element_of($element,@set);

for (my $i=0;$i<@set;$i++)
 {
 if($element eq $set[$i])
 {
 return $i;
 }
 }
}

### End Subroutines

### 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);

my @response=();
my $count=0;

if(@set1>@set2)
{
 print " There is no way that set A={$set1} is a subset of B={$set2} since there are more elements in A than in B. This is like asking if you can fit a football field in a small building. Perhaps you mixed up the two sets? In any event, double check the problem. ";
 goto end;
}

print " To determine if the set A={$set1} is a subset of B={$set2}, we need to determine if EVERY element in A is also in B. If EVERY element in A is also an element of B, then this means that A is a subset of B. This will be denoted as *[Tex \\LARGE A \\subseteq B]. ";

print " So let's go through each element of A={$set1} and see if it is also in B={$set2}: ";

for (my $i=0;$i<@set1;$i++)
{
 print " Question: Is the element \"$set1[$i]\" from set A also in B={$set2}? The answer is ";
 if(is_element_of($set1[$i],@set2))
 {
 my $index=return_index($set1[$i],@set2)+1;
 print "yes (it's the ",num_ordinate($index)," element in B). So let's check that off the list and move to the next element. ";

$count++;
 }
 else
 {
 print "no. Since \"$set1[$i]\" is in A, but NOT in B, this means that A is NOT a subset of B. ";
 #print " We can denote is as *[Tex \\LARGE A \\not\\subseteq B]. ";
 print " So set A={$set1} is NOT a subset of B={$set2} because not all of A is in B. ";
 goto end;
 }
}

if($count==@set1)
{
 print " Since all the answers to the questions above were all \"yes\" (and we've checked all of set A), this means that we've shown that EVERY element in set A is also in set B. So all of A is contained in B. ";
 print " This means that A is a subset of B which is denoted by *[Tex \\LARGE A \\subseteq B]. ";

print " Note: Not only is A a subset of B, A is also a <a href=http://en.wikipedia.org/wiki/Proper_subset>proper subset</a> of B (since A is smaller than B). " if @set1<@set2;
}

end:

==section output

==section check