Party Night

Today is the town's celebration day, when, by tradition, all townspeople take part in special events. Each of them attends a daytime event, where they meet, have fun, and make new friends. Later on, after these events end, a set of evening gatherings are held, and everyone goes to one of them as well. To help the villagers make as many acquaintances as possible, no two people attend both the same daytime and evening gatherings.

Naturally, after so many activities, everyone has a hard time recalling all the details of whom they met; yet people are curious about the social connections that formed. Unfortunately, all they remember is which other townspeople they have crossed paths with at an event, but not when or where. Even these memories might not be fully accurate, so they need your help to determine if the recollections can be logically consistent — or whether someone must have made a mistake (either by forgetting someone present, or thinking they met someone who was not actually there). Can you help them?

For example, in a town with $4$ people, suppose villagers $0$, $1$, and $2$ all recall meeting each other, and villagers $2$ and $3$ recall meeting as well. This information is consistent: there could have been daytime events E_0 and E_1, and evening events G_0, G_1, G_2, where person $0$ attended E_0 and G_0, person $1$ attended E_0 and G_1, person $2$ attended E_0 and G_2, and person $3$ attended E_1 and G_2; this configuration matches the given recollections. However, if persons $0$ and $3$ had also recalled meeting, the information could not be correct.