Claiming myself as a dependent?

I'm currently filing my taxes for this year and I am 19 years old and have been working a full time job for 4 months. On my w-4 I claimed myself as a dependent and have 2 exemptions. My father said that on his taxes he can claim me also and is going to and told me to claim myself as well. If I filed as a dependent on my w-4 can I claim myself on income taxes?