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In this problem, we are examining three fluorine isotopes: F-21, F-18, and F-17. All isotopes of fluorine have an atomic number of 9, meaning they have 9 protons. The mass numbers of the respective isotopes (21, 18, and 17)mean that they have 12, 9, and 8 neutrons, respectively.

Fluorine-21 has a mass number of 21, which means it has 12 neutrons – 3 more than that of stable fluorine-19. To become an isotope with smaller mass number than its own or convert to a smaller element in the periodic table, F-21 can undergo beta-minus (β-) decay, in which a neutron is converted into a proton by emitting an electron (β- particle). This will increase the atomic number by 1 while keeping the mass number the same, leading to the formation of a new element, neon-21.

Fluorine-18 has a mass number of 18, meaning it has one extra neutron compared to stable fluorine-19. To reduce the mass number, it can also undergo beta-minus (β-) decay. In this process, one of the neutrons is converted into a proton, emitting an electron (β- particle). This increases the atomic number by 1 while keeping the mass number the same, resulting in the formation of oxygen-18.

Fluorine-17 has a mass number of 17, meaning it has one fewer neutron than stable fluorine-19. In this case, F-17 can undergo beta-plus (β+) decay or electron capture to increase its mass number. In β+ decay, one proton is converted into a neutron by emitting a positron. This decreases the atomic number by 1 while keeping the mass number the same, resulting in the formation of oxygen-17. Alternatively, F-17 can undergo electron capture, a process where a proton captures one of the atomic electrons and is converted into a neutron. This will lead to a decrease in atomic number and formation of oxygen-17 as well. In conclusion, the possible modes of decay for fluorine-21, fluorine-18, and fluorine-17 are β- decay for F-21, β- decay for F-18, and β+ decay or electron capture for F-17.