Explanation:

Anion Formation:
Anions are formed when atoms gain electrons to achieve a stable electron configuration. The tendency for an atom to form anions depends on its position in the periodic table and its ability to attract electrons. The following factors influence the tendency to form anions:

1. Atomic size: Larger atoms have weaker nuclear attraction, making it easier for them to gain electrons and form anions.
2. Effective nuclear charge: The greater the effective nuclear charge, the stronger the attraction for electrons, making it more difficult for atoms to gain electrons and form anions.
3. Electron affinity: The energy change when an atom gains an electron. Higher electron affinity indicates a stronger tendency to gain electrons and form anions.

Comparison of the Sets:
Let's compare the given sets and analyze their tendencies to form anions.

a) Ga, In, Tl:
These elements belong to Group 13 of the periodic table, also known as the Boron family. They have three valence electrons and tend to lose these electrons to achieve a stable electron configuration. Therefore, they have a tendency to form cations (+3 charge) rather than anions.

b) Na, Mg, Al:
These elements belong to Group 1 and Group 2 of the periodic table. Group 1 elements (alkali metals) have a strong tendency to lose one electron and form cations with a +1 charge. Group 2 elements (alkaline earth metals) have a tendency to lose two electrons and form cations with a +2 charge. Therefore, these elements have a weak tendency to form anions.

c) N, O, F:
These elements belong to Group 15 and Group 16 of the periodic table. Group 15 elements (nitrogen family) have five valence electrons and tend to gain three electrons to achieve a stable electron configuration. Group 16 elements (oxygen family) have six valence electrons and tend to gain two electrons to achieve a stable electron configuration. Group 17 elements (halogens) have seven valence electrons and tend to gain one electron to achieve a stable electron configuration. Therefore, these elements have a strong tendency to gain electrons and form anions.

d) V, Cr, Mn:
These elements belong to the transition metals group and have multiple oxidation states. They tend to lose or gain electrons depending on the reaction conditions. Therefore, their tendency to form anions is not as strong as the elements in group c.

Conclusion:
Based on the analysis, we can conclude that among the given sets, the set N, O, F has the strongest tendency to form anions. These elements belong to Group 15 and Group 16 of the periodic table and have a strong tendency to gain electrons to achieve a stable electron configuration.