Ms. Young and Mr. Dakhlalla are among a number of people who have been detained nationwide for exhibiting what officials say are Islamic State sympathies. In many cases, the authorities say, they have developed their views, in part, by watching online videos and were arrested after creating social media posts that attracted the attention of the F.B.I.

The two were arrested in August 2015 as they prepared to board a flight from Columbus, Miss. The authorities said that in May, the couple had contacted undercover federal agents who were posing online as Islamic State supporters, seeking help in traveling to Syria.

Prosecutors say that Ms. Young had begun to view Islamic State fighters as liberators, and that she had approvingly cited a video that showed militants throwing a man, whom they believed to be gay, off a roof to his death. Prosecutors also said that Ms. Young had expressed approval of a shooting attack in 2015 in Chattanooga, Tenn., that left five United States service members dead.

By May 2015, according to prosecutors, Ms. Young began seeking advice online about how to travel to Syria, and eventually made contact with undercover F.B.I. employees.

At her sentencing, Ms. Young broke down in tears and said that she found what she did “surreal,” and that she had turned to Islam amid an emotional crisis. Ms. Young added that she felt shame for her actions, and sorrow for the humiliation she had caused her family.