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here were going to look at the notion of an indexing set and intersections and unions over indexed sets so lets look at the definition so we want to start with i where that is any set and i really mean any set here there are some usually standard choices for indexing sets but you can really take it to be arbitrary but the one rule that you need is that for all little i and capital i we can produce some set a sub i and then we wanted to find the union over all of these sets and the intersection over all of these sets so the union over the ai as i runs from this whole indexing set capital i so thats going to be everything x that satisfies this rule so x is in aj for at least one j and i so you can think of this at for at least one statement as being like an or statement and then next the intersection of the a i over this indexing set is all x that satisfy this rule so x is in aj for all j and i so here you can think about this for all as like an and statement if you want to relate th