For problems where sets are described as events such as:
In a group of 12 friends, 8 study French, 4 study french only and 2 study neither French nor Cantonese. Let A be the event 'studies French' and let B be the event 'studies Cantonese'.
To my mind, A and B are sets and the elements are people (friends). How are they then also events? Is it because the 12 friends comprise the ""sample space"" and the event is ""sampling""?
A set is any collection of objects (mathematical or not). An event is ""an outcome or defined collection of outcomes of a random experiment"" (well, according to Statistics.com). I don't think it's a contentious subject so I'll quote wikipedia here for the definition of an event: ""In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.""
Where is the experiment in the initial statements? Or am I confusing the sets defined by the text with my own e.g.
Set A={a,b,c,d,e,f,g,h}
Set B={e,f,g,h,i,j}
compliment of the sets = {k,l}
Perhaps the categories are the 'elements' of the sets in this instance?
Set A={any friend who studies French}
Set B={any friend who studies Cantonese}
compliment of the sets = {any friend who studies neither}
I am new to this but I've heard of set builder notation. I'm wondering how to describe ""Let A be the event 'studies French' and let B be the event 'studies Cantonese'."" in set builder in that case.