Frances $(63)$ shared a home all year with her son, Antonio $(41),$ and Antonio's son, Danny $(23).$ They were all U$.$S$.$ citizens, lived in the U$.$S$.$ all year, and all had social security numbers valid for employment. Frances and Antonio worked full$-$time. Danny was a part$-$time student during the year; he took one class at the local community college. Danny also worked part$-$time and had wages of $$6,800.$ No one else lived in the home. Frances had earned income and an adjusted gross income of $$23,459.$ She had no foreign income or investment income. Antonio had earned income and an adjusted gross income of $$32,500.$ He had no foreign income or investment income. Who, if anyone, is eligible to claim and receive the Earned Income Credit?

Both Frances and Antonio.

Either Frances or Antonio but not both.

Frances only.

No one. Child is $23$ not full time and not Frances relative.