I paid for my child's college tuition, $3760.00. Is that deductible?

IRS says:  
Who Can Claim a Dependent's Expenses Generally, in order to claim the tuition and fees deduction for qualified education expenses for a dependent, you must:
1) Have paid the expenses.
2)Claim an exemption for the student as a dependent.

I do not understand #2.
Isn't he my dependent anyway since I paid for all of his support?
He also worked part time and lived at home the entire year. He was 20 years old for ten months in 2014.