Set Notation denoting events
Hey guys just having some trouble with set notation.
A survey is classified as successful if usable data is obtained from it. Let Ai denote the event that at most i repetitions of the survey are required for success. Use set notation to identify the following events:
a) Exactly 1 repetition is required for success
b) At least 2 repetitions are required for success,
c) At least i (where i ≥2) repetitions are required for success
d) Exactly i (where i ≥2) repetitions are required for success
e) Is it true that A1OR A2 = A2?
f) What then is A1AND A2AND A3?
Ok so I am pretty sure that e is true because A1 is a proper subset of A2? Therefore the union of them would be equal to just the elements of A2
For a I know that A1 is a subset of all the successive sets and so I would need to negate the subsets from the subsequent sets but I am not sure how to do this. Something along the lines of Ai = (i:i=1)? A friend of mine said something about A1 OR (A0)c
For b I am not sure at all the best I could do was A2ORÖAi = (i:i>2)
For c it might be Big ORi Ai = (i:i≥2)
D and f I donít really have any idea.
I know the difference between exactly and at least but am not sure how to apply it in this problem. I have this horrible feeling that everything I just wrote is wrong haha
If someone could steer me in the right direction that would be great.
(Iím new to set notation) Should there be a different variable in the brackets?