Greedy algorithm...

At a conference, your goal is to attend the smallest subset of events that conflict with every other event that you could be attending $-$ that way, if your boss asks you why you didn't attend more events, you'll be able to tell her that you couldn't attend any other events due to scheduling conflicts.

Formally, the conference events are given as an input list V $,$ and each event vi is defined by a start time and finish time $($si$,$ fi$).$ Your goal is to select the smallest subset of events such that every event in V overlaps with at least one of your chosen events. An event vi $=(1,4)$ overlaps with the event vj $=(3,5)$ but not with the event vk $=(4,6).$

How to describe a greedy algorithm that finds an optimal solution?

For example, the optimal solution for these events:

$$ v$1=(1,3)$;

$$ v$2=(2,4)$;

$$ v$3=(3,4)$;

$$ v$4=(3,5)$;

$$ v$5=(4,5)$;

$$ v$6=(4,6)$;

$$ v$7=(5,7).$

consists of the events v$2,$ v$6$

Please provide detailed, step by step help.