Mel and Cindy Gibson's 12-year-old daughter Rachel was abducted on her way home from school on March 15, 2016.Police reports indicated that a stranger had physically dragged Rachel into a waiting car and sped away. Everyone hoped that the kidnapper and Rachel would be located quickly. However, as of the end of the year, Rachel was still missing. The police were still pursuing several promising leads and had every reason to believe that Rachel was still alive. In 2017, Rachel was returned safely to her parents. 

a. Are the Gibsons allowed to claim an exemption deduction for Rachel in 2016 even though she only lived in the Gibson's home for two and one half months? Explain and cite your authority.

b. Assume the original facts except that Rachel is unrelated to the Gibsons, but she has been living with them since January 2011. The Gibsons have claimed a dependency exemption for Rachel for the years 2011 through 2015. Are the Gibsons allowed to claim a dependency exemption for Rachel in 2016? Explain and cite your authority.