Education

That would be difficult  to answer without further information. 

First would be to determine if the student supplied more than half of their own support. Since they didn't even pay rent I would assume no, so they are a dependent. 

Next, whose dependent is the student? 

You say "relative". Could the student be their "Qualifying Child?" "The student must be their son, daughter, stepchild, eligible foster child, brother, sister, half-brother, half-sister, stepbrother, stepsister, adopted child or a descendent of any of them" to be their qualifying child, so if not, the student would need to be their qualifying relative in which case the student would need to have earned less than 4,300.

For you the time at the relatives could be considered as living at home if the student was only away because he/she was attending school. This would include time not actually in class and even working a job if the intent is to return home when finished with school. Then you would still claim the student as your dependent. 

It's a bit subjective. Below is a link to an IRS interview which might help. 

You can claim a person as your dependent if they meet the requirements of being your “Qualifying Child” or Qualifying Relative”

These terms can seem misleading since a “Qualifying Child” does not need to be your child and a “Qualifying Relative” does not be related to you.

A “Qualifying Child is a person that meet these tests:

• WHO IS THE PERSON? The person must be your son, daughter, stepchild, eligible foster child, brother, sister, half-brother, half-sister, stepbrother, stepsister, adopted child or a descendent of any of them.
• HOW OLD IS THE PERSON? The person must be under age 19 or, if a full-time student, under age 24. They must also be younger than you (or either you or your spouse if you’re filing Married Filing Jointly)

There is no age limit if your child is permanently and totally disabled.

• WHERE DOES THE PERSON LIVE? The person must have lived with you for more than half the tax year, but several exceptions apply such as school and military service.
• WHO SUPPORTS THE PERSON? The person cannot have provided more than half of their own support. It doesn’t matter how much they earned.
• HOW WILL THIS PERSON FILE THEIR TAX RETURN (IF THEY HAVE TO FILE ONE)? The person can’t be filing a Married Filing Jointly tax return, although there is an exception to that.

A QUALIFYING RELATIVE IS A PERSON THAT MEETS THESE TESTS:

                This person can’t be a qualifying child to you or anyone else.

                This person must have lived with you OR be a relative of yours.

                This person must have gross income of less than $4,300

                This person must have gotten more than half their support from you.

IRS INTERVIEW